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Problem 601

12/16
If the blue graph is $f(x)=x^{2}$ then the red must be... $g(x)=x^{2}+5$ $g(x)=(x-5)^{2}$ $g(x)=(x+5)^{2}$ $g(x)=x^{2}-5$

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Problem 602

Solve the equation. (Enter your answers as a comma-separated list.) $\begin{array}{l} x^{2}+13 x+36=0 \\ x=\square \end{array}$

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Problem 603

(1 point) Which function has a maximum value? a. $f(x)=1.2(x+3)^{2}+1.5$ b. $f(x)=-3(x-12)^{2}+5$ c. $f(x)=2(x-15)^{2}-3$ (c.) $f(x)=(x-13)^{2}+12$

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Problem 604

Short Answer
10. (3 points) Sketch the graph of $f(x)=-(x-4)^{2}+2$ , then state the domain and range of the function.

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Problem 605

II. Based on the methods we have discussed in class so far, which of the following methods cannot be used to solve the following equations? You may choose more than one answer. a. $x^{2}-27=0$
Square Roots Factoring Quadratic Formula Explain your reasoning using mathematical language:

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Problem 606

(2 points) Determine the equation that defines a quadratic function with $x$ -intercepts located at $(-9,0)$ and $(-2,0)$ and a $y$ -intercept of $(0,18)$ .

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Problem 607

Solve the system $\begin{array}{l} x^{2}+x y=1 \\ x y+y^{2}=288 \end{array}$
Your answer is $\begin{array}{ll} x_{1}=\square \\ x_{2}=\square & y_{1}=\square \\ \square & y_{2}=\square \\ \square & \text { and } \\ \square & \text { with } x_{1}<x_{2} \end{array}$ Submit answer Next item

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Problem 608

The sum of two distinct numbers is 39 and the product of the two numbers is 360 . Find the two numbers using a system of nonlinear equations. Enter your answers as a comma-separated list.
Answer: $\square$
Submit answer

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Problem 609

Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms. Second-degree, with zeros of -6 and 2 , and goes to $-\infty$ as $x \rightarrow-\infty$ .
Answer

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Problem 610

3. ( 3 points) Determine the equation that defines a quadratic function with $x$ -intercepts located at $(-9,0)$ and $(-2$ , 0 ) and a $y$ -intercept of $(0,18)$ .

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Problem 611

$b^{2} - 13b + 42$

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Problem 612

(VCAA-type question) The given table of values follows the rule: $y=k x^{2}+c$ . \begin{tabular}{|c|c|c|c|c|} \hline $x$ & 1 & 2 & 3 & 4 \\ \hline $y$ & 4.5 & 9 & 16.5 & 27 \\ \hline \end{tabular}
The values of $k$ and $c$ respectively are: A 1 and 5 B 1.5 and 3 C 2 and 11 D 3 and 6 E 5 and 1.5

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Problem 613

$m^{2} + m - 42$

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Problem 614

Question Watch Video Show
Express $(x-12)^{2}$ as a trinomial in standard form. Answer Attempt 1 out of 2

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Problem 615

$x^{2}-7 x-60$

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Problem 616

Solve the equation using the quadratic formula.
1. $5 x^{2}+x-3=0$
2. $8 x^{2}+6 x+5=0$
3. $2 x^{2}-x-4=0$
4. $x^{2}+16 x+64=0$
5. $x^{2}-8 x+12=0$

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Problem 617

Use the square root property to solve the quadratic equation. $4 x^{2}-8=0$

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Problem 618

$\begin{array}{l}f(x)=(4-x)^{2} \\ f(11)=\square\end{array}$

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Problem 619

$\begin{array}{l}f(x)=(1+x)^{2} \\ f(9)=\square\end{array}$

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Problem 620

$\begin{array}{l}f(y)=y^{2}-10 y \\ f(s+2)=\end{array}$

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Problem 621

Solve the equation $3 x^{2}+9 x+2=0$ to the nearest tenth.

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Problem 622

Write an equation for the quadratic graphed below $x$ -intercepts: $(-1,0)$ and $(3,0) . y$ -intercept: $(0,-3)$ $y=$ $\square$

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Problem 623

NASA launches a rocket at $t=0$ seconds. Its height, in meters above sea-level, as a function of time is given by $h(t)=-4.9 t^{2}+295 t+339$ .
Assuming that the rocket will splash down into the ocean, at what time does splashdown occur?
The rocket splashes down after $\square$ seconds.
How high above sea-level does the rocket get at its peak?
The rocket peaks at $\square$ meters above sea-level.

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Problem 624

Answer the questions below about the quadratic function. $g(x)=x^{2}+8 x+17$
Does the function have a minimum or maximum value? Minimum Maximum
What is the function's minimum or maximum value? $\square$
Where does the minimum or maximum value occur? $x=$ $\square$

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Problem 625

A ball is thrown vertically upward. After $t$ seconds, its height $h$ (in feet) is given by the function $h(t)=48 t-16 t^{2}$ . After how long will it reach its maximum height?
Do not round your answer.
Time: $\square$ seconds

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Problem 626

$x^{2}+2 x-5=0$

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Problem 627

b. To factor with tiles (like you did in part (a)), you need to determine how to arrange the tiles to form a rectangle. Using a generic rectangle to factor requires a different process.
Miguel wants to use a generic rectangle to factor $3 x^{2}+10 x+8$ . He knows that $3 x^{2}$ and 8 go into the rectangle in the locations shown at right. Finish the rectangle by deciding how to place the ten $x$ -terms. Then write the area as a product. \begin{tabular}{|l|l|} \hline & 8 \\ \hline $3 x^{2}$ & \\ \hline \end{tabular}

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Problem 628

A ball is thrown vertically upward. After $t$ seconds, its height $h$ (in feet) is given by the function $h(t)=112 t-16 t^{2}$ . After how long will it reach its maximum height?
Do not round your answer.
Time: $\square$ seconds

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Problem 629

DID YOU HEAR... \begin{tabular}{|l|l|l|l|l|l|l|} \hline I. The & 2. Sad & 3. & 4. & 5. & 6. & 7. \\ \hline 8. & 9. & 10. & of & II. & 12. & 13. \\ \hline \end{tabular}
Solve the equation by factoring. Write the word next to the answer in the box that contalns the exercise number.
1. $a^{2}-8 a=-15$ $a=3 \quad a=5$
2. $y^{2}+6 y=7$ $y=-2 \quad y=1$ The Sad
3. $k^{2}-10=9 k$
4. $w^{2}=13 w$ $w=0 \quad w=13$
5. $11 x=-x^{2}-24$
6. $d^{2}=50-23 d$
7. $3 p^{2}-14 p=5$
8. $2 m^{2}+14=11 m$
9. $8-3 t=5 t^{2}$
10. $16 h^{2}=25$ II. $25 b+11=-6 b^{2}$
12. $36 u=9 u^{2}$
13. $12 q^{2}=17 q+5$
14. $9=12 x-4 x^{2}$
Quadratic Equations and Functions: PUNCHLINE • Algebra • E
Solving Quadratic Equations by Factoring (Equations Not in Standard Form) @2006 Marcy Math • Algebra 14.8

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Problem 630

c. Kelly wants to find a shortcut to factor $2 x^{2}+7 x+6$ . She knows that $2 x^{2}$ and 6 go into the rectangle in the locations shown at right. She also remembers Casey's pattern for diagonals. Without actually factoring yet, what do you know about the missing two parts of the generic rectangle? product sum e. Use your results from the Diamond Problem to complete the generic rectangle for $2 x^{2}+7 x+6$ , and then write the area as a product of factors.

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Problem 631

4 Use substitution to solve if $d=5.5$ $4.5+\left(d^{2}+45\right)-d$

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Problem 632

Non-Calculator Q1. Express $4 x^{2}-12 x+14$ in the form $a(x+b)^{2}+c$

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Problem 633

```latex A manufacturer of tennis rackets finds that the total cost $C(x)$ (in dollars) of manufacturing $x$ rackets/day is given by $C(x)=400+4x+0.0001x^{2}$ . Each racket can be sold at a price of $p$ dollars, where $p$ is related to $x$ by the demand equation $p=10-0.0004x$ . If all rackets that are manufactured can be sold, find the daily level of production that will yield a maximum profit for the manufacturer. ```

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Problem 634

49. Maximizing Profit A division of Chapman Corporation manufactures a pager. The weekly fixed cost for the division is $\$ 20,000$ , and the variable cost for producing $x$ pagers per week is $V(x)=0.000001 x^{3}-0.01 x^{2}+50 x$ dollars. The company realizes a revenue of $R(x)=-0.02 x^{2}+150 x \quad(0 \leq x \leq 7500)$ dollars from the sale of $x$ pagers/week. Find the level of production that will yield a maximum profit for the manufacturer. Hint: Use the quadratic formula.

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Problem 635

An astronaut on the moon throws a baseball upward. The astronaut, is $6 \mathrm{ft}, 6 \mathrm{in}$ . tall, and the initial velocity of the ball is 50 ft per sec . The height s of the ball in feet is given by the equation $\mathrm{s}=-2.7 \mathrm{t}^{2}+50 \mathrm{t}+6.5$ , where t is the number of seconds after the ball was thrown. Complete parts $a$ and $b$ . a. After how many seconds is the ball 20 ft above the moon's surface?
After $\square$ seconds the ball will be 20 ft above the moon's surface. (Round to the nearest hundredth as needed. Use a comma to separate answers as needed.)

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Problem 636

An astronaut on the moon throws a baseball upward. The astronaut, is $6 \mathrm{ft}, 6 \mathrm{in}$ . tall, and the initial velocity of the ball is 50 ft per sec . The height s of the ball in feet is given by the equation $s=-2.7 \mathrm{t}^{2}+50 \mathrm{t}+6.5$ , where $t$ is the number of seconds after the ball was thrown. Complete parts $a$ and $b$ . a. After how many seconds is the ball 20 ft above the moon's surface?
After $\square$ seconds the ball will be 20 ft above the moon's surface. (Rounchto the nearest hundredth as needed. Use a comma to separate answers as needed.)

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Problem 637

Solve for $u$ . $(u-3)^{2}=2 u^{2}-10 u-12$
If there is more than one solution, separate them with commas. $u=$ $\square$

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Problem 638

1. Determine the value of $k$ such that $f(x)=2 x^{2}+8 x+11-k$ has only one zero.

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Problem 639

2. find the zeres and verten for the function $f(x)=3 x^{2}+12 x-135$

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Problem 640

Find the square. Simplify your answer. $(4 z-4)^{2}$

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Problem 641

Determine, without graphing, whether the given quadratic function has a maximum value or a mir $f(x)=-4 x^{2}-16 x-9$
The quadratic function has a $\square$ value. minimum maximum

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Problem 642

Find the square. Simplify your answer. $(4 h+3)^{2}$

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Problem 643

odule 5 Final culz Question 4 of 12 list
For the quadratic function $f(x)=x^{2}+6 x$ , answer parts (a) through ( $f$ ). (a) Find the vertex and the axis of symmetry of the quadratic function, and determine whether the graph is concave up or concave down.
The vertex is $\square$ (Type an ordered pair, using integers or fractions.) What is the equation of the axis of symmetry? The axis of symmetry is $\square$ (Use integers or fractions for any numbers in the equation.) Is the graph concave up or concave down? Concave down Concave up (b) Find the $y$ -intercept and the $x$ -intercepts, if any.
What is the $y$ -intercept? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The $y$ -intercept is $\square$ . (Type an integer or a simplified fraction.) B. There is no y-intercept.
What is the x-intercept? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The $x$ -intercept(s) is/are $\square$ . (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. There are no $x$ -intercepts. (c) Use parts (a) and (b) to graph the function.
Use the graphing tool to graph the function. Click to enlarge graph (d) Find the domain and the range of the quadratic function.
The domain of $f$ is $\square$ (Type your answer in interval notation.) The range of $f$ is $\square$ . (Type your answer in interval notation.) (e) Determine where the quadratic function is increasing and where it is decreasing.
The function is increasing on the interval $\square$ . (Type your answer in interval notation.) The function is decresasing on the interval $\square$ . (Type your answer if interval notation.) (f) Determine where $f(x)>0$ and where $f(x)<0$ . Select the correct choice below and fill in the answer box(es) within your choice.

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Problem 644

find + simplify $f(x)=x^{2}-6$

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Problem 645

Determine if the equation $x^2 - y = 9$ defines a function.

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Problem 646

Find the equation of the axis of symmetry for the parabola $y=\frac{-3}{2} x^{2}-9 x-8$

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Problem 647

$2 \cos ^{2} x-5 \cos x+2=0$

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Problem 648

Question 2, 7.1.79 Part 1 of 3 HW Score: $5.88 \%, 1$ of 17 points Points: 0 of 1 Save
The function models the number of accidents, $f(x)$ , per 50 million miles driven as a function of a driver's age, $x$ , in years, where $x$ includes drivers from ages 16 through 74 , inclusive. The graph of $f$ is shown. Find and interpret $f(69)$ . Identify this information as a point on the graph of $f$ .
Find $\mathrm{f}(69)$ . $f(69)=$ $\square$ (Simplify your answer. Type an integer or a decimal.)

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Problem 649

Use the quadratic formula to solve. Express your answer in simplest form. $-3 r^{2}+9 r+4=-5 r^{2}$

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Problem 650

Use the quadratic formula to solve. Express your answer in simplest form. $6 w^{2}-7 w-3=0$

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Problem 651

Use the quadratic formula to solve. Express your answer in simplest form $3 c^{2}+14 c-8=4 c$

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Problem 652

Solve using the quadratic formula and find the zeros $f(x)=(x-1)\left(x^{2}-x+1\right)$

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Problem 653

For a certain stretch of road, the distance $d$ (in ft ) required to stop a car that is traveling at speed $v$ (in mph) before the brakes are applied can be approxim by $d(v)=0.08 v^{2}+2 v$ . Find the speeds for which the car can be stopped within 300 ft .
The solution set in interval notation is $\square$

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Problem 654

17. A soccer ball is kicked with an initial vertical velocity of $64 \mathrm{ft} / \mathrm{s}$ . The function $h(t)=-16 t^{2}+64$ models the height $h$ (in feet) of the soccer ball at time $t$ (in seconds). When does the soccer ball reach the ground?

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Problem 655

Given the expression below, state the method that would be used to factor the expression. Then, factor it completely. $4 x^{2}-9$
Method: $\square$
Factored form: [Select] $\square$

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Problem 656

Use the information provided to write the factored form equation of each parabola. zeros: $(3,0),(5,0)$ , Passes through: $(4,1)$ Find the 'a' value: $\square$
Type in the entire function using the format: $y=a(x-p)(x-q)$ with no spaces. $\square$

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Problem 657

Write the quadratic function in standard form. $y=4(x-3)(x-5)$
Find the values of $\mathrm{a}, \mathrm{b}$ , and c for the function $y=a x^{2}+b x+c$ .
What is the value of $a$ ? $\square$
What is the value of $b$ ? $\square$
What is the value of $c$ ? $\square$

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Problem 658

Drow Graph of function for: $\begin{array}{l} f(x)=1 / 3 x^{2}-2 / 3 x-5 \\ \text { vertex: }\left(1,-\frac{16}{3}\right) \text { or }(1,-5,3) \\ y \text { - intercept: }(0,-5) \\ x \text { - intercepts: }(5,0) \text { and }(-3,0) \end{array}$

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Problem 659

1 2 3 4 5 6 7 8 $y$ IU
What is the first step when rewriting $y=6 x^{2}+18 x+14$ in the form $y=a(x-h)^{2}+k$ ? 16 must be factored from $18 x+14$ $x$ must be factored from $6 x^{2}+18 x$ 6 must be factored from $6 x^{2}+14$ 6 must be factored from $6 x^{2}+18 x$

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Problem 660

The product of two numbers is 240 . The first number is 8 less than the second number. Which equation can be used to find $x$ , the lesser number? $x(x-8)=240$ $x(x+8)=240$ $x^{2}-8=240$ $x^{2}+8=240$

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Problem 661

$x^{2}-4 \geqslant 0$

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Problem 662

Graph the parabola. $y=3 x^{2}-12 x+5$
Plot five points on the parabola: the vertex, two points to the left of the vertex, and two points to the right of the vertex. Then click on the graph-a-function button.

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Problem 663

$\text{Given the axis of symmetry } (3, 4) \text{ and point } (5, 0), \text{ find the equation of the parabola in vertex form.}$

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Problem 664

Let $\mathrm{p}, \mathrm{q}$ be the roots of the equation $3 x^{2}-9 x+k=0$ such that $\left(p^{2}+q^{2}\right)$ and $\left(\frac{1}{p}+\frac{1}{q}\right)$ are the roots of the equation $x^{2}+2 m x+m=0$ . Then what is the value of $k(2 k+9) ?$

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Problem 665

Graphing with Intercept Form Graph the function. Label the vertex and the $\boldsymbol{x}$ -intercepts.
44. $y=(x-3)(x-5)$
45. $y=-(x+2)(x-2)$
46. $y=(x+1)(x$
47. $y=-2(x-1)(x-2)$
48. $y=\frac{1}{2}(x+4)(x-2)$
49. $y=\frac{1}{3}(x-3)($
50. $y=3(x+3)(x-1)$
51. $y=4(x-7)(x+2)$
52. $y=x(x-5)$

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Problem 666

48. $y=\frac{1}{2}(x+4)(x-2)$

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Problem 667

8.2 Solve the following inequalities analytically, using sign diagrams. Verify your answer graphically (a) $x^{2}-2 \leq 2 x$ (b) $12 x-4 \geq 9 x^{2}$

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Problem 668

$f(x)=-2 x^{2}-8 x-4$
Does the function have a minimum or maximum value? Minimum Maximum
What is the function's minimum or maximum value? $\square$ Where does the minimum or maximum value occur? $x=-12$

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Problem 669

Solve using the principle of zero products. $c(c+5)=0$
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution(s) is/are $\mathrm{c}=$ $\square$ . (Use a comma to separate answers as needed. Type each solution only once.) B. There is no solution.

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Problem 670

18. A ball is thrown into the air follows the quadratic function $h(t)=-8 t^{2}+16 t$ , where the time $t$ is measured in seconds and $h(t)$ , measured in feet, is the height above ground level. a) What is the independent variable? b) What is the dependent variable? c) At what time the ball will reach its maximum height? d) What is the maximum height the ball will reach? e) What are the coordinates of the vertex? f) What are the coordinates of $y$ -intercept? g) What are the coordinates of $x$ -intercept(s)? h) What is the axis of symmetry of function $h(t)$ ? i) Is function $h(t)$ even, odd, or neither and why?

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Problem 671

19. A ball is thrown into the air follows the quadratic function $h(t)=-5 t^{2}+19 t+20$ , where the time $t$ is measured in seconds and $h(t)$ , measured in feet, is the height above ground level. a) What is the independent variable? b) What is the dependent variable? c) At what time the ball will reach its maximum height? d) What is the maximum height the ball will reach? e) What are the coordinates of the vertex? f) What are the coordinates of $y$ -intercept? g) What are the coordinates of $x$ -intercept(s)? h) What is the axis of symmetry of function $h(t)$ ? i) Is function $h(t)$ even, odd, or neither and why?

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Problem 672

$\begin{array}{l} \text { 2. } y=x^{2}-6 x+5 \\ y=12 \\ \begin{array}{l} 12=x^{2}-6 x+5 \\ -12 \quad-12 \end{array} \\ x^{2}-6 x-7=0 \end{array}$

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Problem 673

Evaluate the expression when $c=3$ . $c^{2}-5 c+2$

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Problem 674

uation $(n-2)^{2}=49$ reasoning.

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Problem 675

Find the minimum value of the parabola $y=x^{2}+8$ .
Simplify your answer and write it as a proper fraction, improper fraction, or integer. $\square$ Submit

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Problem 676

Find the $y$ -intercept of the parabola $y=4 x^{2}+8 x$ .
Simplify your answer and write it as a proper fraction, improper fraction, or integer. $\square$ Submit

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Problem 677

Find the vertex of the parabola $y=-9 x^{2}$
Simplify both coordinates and write them as proper fractions, improper fractions, or integers. $\square$ $\square$ Submit

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Problem 678

Find the $y$ -intercept of the parabola $y=4 x^{2}+2 x+4$
Simplify your answer and write it as a proper fraction, improper fraction, or integer. $\square$ Submit

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Problem 679

5. a) Determine the equation in vertex form of a function that has a range of $(-\infty, 14]$ and $x$ -intercepts at -5 and 1. (3 marks)

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Problem 680

Stuffco Industries makes model airplanes and wants to know their average cost and revenue at a production level of 300 . If their cost function is $C(x)=2700+65 x+x^{2}$ and their revenue function is $R(x)=530 x-x^{2}$ , what is their average cost and revenue?
Select the correct answer below: Average cost: $\$ 274 ;$ Average Revenue: $\$ 530$ . Average cost: $\$ 380$ ; Average Revenue: $\$ 250$ . Average cost: $\$ 374$ ; Average Revenue: $\$ 230$ . Average cost: $\$ 112,200 ;$ Average Revenue: $\$ 69,000$

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Problem 681

Page 1: 1 2 3 Question 1 (1 point) -- -- --
4 5 6 $\square$ -- 7 8 9
10 11 12
13

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Problem 682

What translation of $y=x^{2}$ results in a new function with vertex $(-3,6) ?$ 3 units left and 6 units up 3 units right and 6 units down 6 units right and 3 units down 6 units left and 3 units up

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Problem 683

For the following set of 4 points: $(0,1),(2,2),(4,0),(-2,1)$ (10 Points) find the line that contains the $1^{\text {st }}$ two points $\frac{2-1}{2-0}=\frac{1}{2}$ $\begin{array}{c} y-1=1 / 2(x-0) \\ y+1=1 / 2 x \\ +1+1 \\ y=1 / 2 x+1 \end{array}$ 60 b) (15 points) find the quadratic that contains the first 3 points

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Problem 684

Graph the function. $f(x)=-2 x^{2}+3$
Plot five points on the graph of the function: one point with $x=0$ , two points with negative $x$ -values, and two points with positive $x$ -values. Then click on the graph-a-function button.

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Problem 685

Graph the function. $f(x)=-4 x^{2}+5$
Plot five points on the graph of the function: one point with $x=0$ , two points with negative $x$ -values, and two points with positive $x$ -values. Then click on the graph-a-function button.

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Problem 686

$(x+4)^{2}+8=0$

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Problem 687

Factor the trinomial, or state that the trinomial is prime. $2 x^{2}-17 x+30$
Select the correct choice below and, if necessary, fill in any answer boxes within your choice. A. $2 x^{2}-17 x+30=$ $\square$ (Factor completely.) B. The trinomial is prime.

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Problem 688

1. A rocket is fired vertically upward with an initial velocity of $29 \mathrm{~m} / \mathrm{s}$ . Final its. a. maximum altitude b. hang time.
2. A pool ball leaves a 0.60 -meter high table with an initial horizontal velocity of $2.4 \mathrm{~m} / \mathrm{s}$ . Determine the: a. time required for the pool ball to fall to the ground b. horizontal distance from the table's edge.
3. A soccer ball is kicked horizontally off a 22.0-meter high hill and lands a distance of 35 meters from the edge of the hill. Determine the: a. initial horizontal velocity b. final velocity (magnitude and direction)

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Problem 689

4) $y=-2 x^{2}-8 x-4$

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Problem 690

5) $y=\frac{1}{2} x^{2}+2 x+5$ 7) $y=2 x^{2}-8 x+4$ 6) $y=-x^{2}+4 x$ 8) $y=2 x^{2}+8 x+10$

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Problem 691

Bass, LaDasia 8th Math - Term 2, Assess 3 3 of 24 1 2 3 4 5 6
The graph of a function is given by the equation $y=-2 x^{2}+4$ . Which statement about the graph of the function is correct? The graph of the function is linear because it has a constant rate of change of -2 . The graph of the function is linear because it has a constant rate of change of 4 . The graph of the function is nonlinear because it contains pointy that are not on a straight line. The graph of the function is nonlinear because it contains points that are on a straight line that does not pass through the origin.

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Problem 692

Question 3 5 pts
A fence is to be built to enclose a rectangular area of 1250 square feet. The fence along three sides is to be made of material that costs $\$ 3$ per foot. The material for the fourth side costs $\$ 9$ per foot. Find the dimensions of the rectangle that will allow for the most economical fence to be built.
The short side is $\qquad$ ft and the long side is $\qquad$ ft. The short side is 25 ft and the long side is 50 ft . The short side is 10 ft and the long side is 125 ft . The short side is 75 ft and the long side is 450 ft . The short side is 5 ft and the long side is 250 ft .

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Problem 693

Directions Factor each trinomial. Identify the binomial factors from below and record the number with the color. Color the picture according to your answers. Staple all work to this paper. Trinomial A: 2x²+5x-42 Trinomial C: 4x²+5x+1 Trinomial B: 5x2 +14x-3 Trinomial D: 3x²-25x-18 Trinomial E: 3x²+16x+16 Trinomial F: 10x²-3x-4 Trinomial G: 2x²-5x+3 Trinomial H: 12x²-13x+3 Trinomial : 6x2-x-15 Trinomial J: 5x²-13x+6 Trinomial K: 2x²+9x+10 Trinomial L: 6x²+31x+5

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Problem 694

20. State which of the following quadratic functions is in standard form and which is in vertex form. Then find the coordinates of the vertex for each one. A) $s(x)=-(x+5)^{2}-8$ B) $g(x)=-4+3 x-2 x^{2}$

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Problem 695

Use the elimination method to find all solutions of the system. Write the solution(5) as a list of ordered pairs. $\left\{\begin{array}{l} x^{2}-4 y=32 \\ x^{2}+2 y=8 \end{array}\right.$

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Problem 696

Factor the following expression completely: $y^{2}-2 y-80=$ $\square$

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Problem 697

Factor the following expression completely: $4 w^{2}-44 w+112=$ $\square$

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Problem 698

Factor: $x^{2}+11 x+28$

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Problem 699

Factor $36 x^{2}-49$

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Problem 700

Fill in the gaps to factorise this expression. $x^{2}+4 x=x\left(\_+\square\right)$

See Solution

Quadratics

Problem 601

12/16If the blue graph is f(x)=x2f(x)=x^{2}f(x)=x2 then the red must be... g(x)=x2+5g(x)=x^{2}+5g(x)=x2+5 g(x)=(x−5)2g(x)=(x-5)^{2}g(x)=(x−5)2 g(x)=(x+5)2g(x)=(x+5)^{2}g(x)=(x+5)2 g(x)=x2−5g(x)=x^{2}-5g(x)=x2−5

Problem 602

Solve the equation. (Enter your answers as a comma-separated list.) x2+13x+36=0x=□\begin{array}{l} x^{2}+13 x+36=0 \\ x=\square \end{array}x2+13x+36=0x=□​

Problem 603

(1 point) Which function has a maximum value? a. f(x)=1.2(x+3)2+1.5f(x)=1.2(x+3)^{2}+1.5f(x)=1.2(x+3)2+1.5 b. f(x)=−3(x−12)2+5f(x)=-3(x-12)^{2}+5f(x)=−3(x−12)2+5 c. f(x)=2(x−15)2−3f(x)=2(x-15)^{2}-3f(x)=2(x−15)2−3 (c.) f(x)=(x−13)2+12f(x)=(x-13)^{2}+12f(x)=(x−13)2+12

Problem 604

Short Answer10. (3 points) Sketch the graph of f(x)=−(x−4)2+2f(x)=-(x-4)^{2}+2f(x)=−(x−4)2+2, then state the domain and range of the function.

Problem 605

Problem 606

(2 points) Determine the equation that defines a quadratic function with xxx-intercepts located at (−9,0)(-9,0)(−9,0) and (−2,0)(-2,0)(−2,0) and a yyy-intercept of (0,18)(0,18)(0,18).

Problem 607

Problem 608

The sum of two distinct numbers is 39 and the product of the two numbers is 360 . Find the two numbers using a system of nonlinear equations. Enter your answers as a comma-separated list.Answer: □\square□Submit answer

Problem 609

Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms. Second-degree, with zeros of -6 and 2 , and goes to −∞-\infty−∞ as x→−∞x \rightarrow-\inftyx→−∞.Answer

Problem 610

3. ( 3 points) Determine the equation that defines a quadratic function with xxx-intercepts located at (−9,0)(-9,0)(−9,0) and (−2(-2(−2, 0 ) and a yyy-intercept of (0,18)(0,18)(0,18).

Problem 611

b2−13b+42b^{2} - 13b + 42b2−13b+42

Problem 612

Problem 613

m2+m−42 m^{2} + m - 42 m2+m−42

Problem 614

Question Watch Video ShowExpress (x−12)2(x-12)^{2}(x−12)2 as a trinomial in standard form. Answer Attempt 1 out of 2

Problem 615

x2−7x−60x^{2}-7 x-60x2−7x−60

Problem 616

Solve the equation using the quadratic formula.1. 5x2+x−3=05 x^{2}+x-3=05x2+x−3=02. 8x2+6x+5=08 x^{2}+6 x+5=08x2+6x+5=03. 2x2−x−4=02 x^{2}-x-4=02x2−x−4=04. x2+16x+64=0x^{2}+16 x+64=0x2+16x+64=05. x2−8x+12=0x^{2}-8 x+12=0x2−8x+12=0

Problem 617

Use the square root property to solve the quadratic equation. 4x2−8=04 x^{2}-8=04x2−8=0

Problem 618

f(x)=(4−x)2f(11)=□\begin{array}{l}f(x)=(4-x)^{2} \\ f(11)=\square\end{array}f(x)=(4−x)2f(11)=□​

Problem 619

f(x)=(1+x)2f(9)=□\begin{array}{l}f(x)=(1+x)^{2} \\ f(9)=\square\end{array}f(x)=(1+x)2f(9)=□​

Problem 620

f(y)=y2−10yf(s+2)=\begin{array}{l}f(y)=y^{2}-10 y \\ f(s+2)=\end{array}f(y)=y2−10yf(s+2)=​

Problem 621

Solve the equation 3x2+9x+2=03 x^{2}+9 x+2=03x2+9x+2=0 to the nearest tenth.

Problem 622

Write an equation for the quadratic graphed below xxx-intercepts: (−1,0)(-1,0)(−1,0) and (3,0).y(3,0) . y(3,0).y-intercept: (0,−3)(0,-3)(0,−3) y=y=y= □\square□

Problem 623

Problem 624

Answer the questions below about the quadratic function. g(x)=x2+8x+17g(x)=x^{2}+8 x+17g(x)=x2+8x+17Does the function have a minimum or maximum value? Minimum MaximumWhat is the function's minimum or maximum value? □\square□Where does the minimum or maximum value occur? x=x=x= □\square□

Problem 625

A ball is thrown vertically upward. After ttt seconds, its height hhh (in feet) is given by the function h(t)=48t−16t2h(t)=48 t-16 t^{2}h(t)=48t−16t2. After how long will it reach its maximum height?Do not round your answer.Time: □\square□ seconds

Problem 626

x2+2x−5=0x^{2}+2 x-5=0x2+2x−5=0

Problem 627

Problem 628

A ball is thrown vertically upward. After ttt seconds, its height hhh (in feet) is given by the function h(t)=112t−16t2h(t)=112 t-16 t^{2}h(t)=112t−16t2. After how long will it reach its maximum height?Do not round your answer.Time: □\square□ seconds

Problem 629

Problem 630

Problem 631

4 Use substitution to solve if d=5.5d=5.5d=5.5 4.5+(d2+45)−d4.5+\left(d^{2}+45\right)-d4.5+(d2+45)−d

Problem 632

Non-Calculator Q1. Express 4x2−12x+144 x^{2}-12 x+144x2−12x+14 in the form a(x+b)2+ca(x+b)^{2}+ca(x+b)2+c

Problem 633

Problem 634

Problem 635

Problem 636

Problem 637

Solve for uuu. (u−3)2=2u2−10u−12(u-3)^{2}=2 u^{2}-10 u-12(u−3)2=2u2−10u−12If there is more than one solution, separate them with commas. u=u=u= □\square□

Problem 638

1. Determine the value of kkk such that f(x)=2x2+8x+11−kf(x)=2 x^{2}+8 x+11-kf(x)=2x2+8x+11−k has only one zero.

Problem 639

2. find the zeres and verten for the function f(x)=3x2+12x−135f(x)=3 x^{2}+12 x-135f(x)=3x2+12x−135

Problem 640

Find the square. Simplify your answer. (4z−4)2(4 z-4)^{2}(4z−4)2

Problem 641

Determine, without graphing, whether the given quadratic function has a maximum value or a mir f(x)=−4x2−16x−9f(x)=-4 x^{2}-16 x-9f(x)=−4x2−16x−9The quadratic function has a □\square□ value. minimum maximum

Problem 642

Find the square. Simplify your answer. (4h+3)2(4 h+3)^{2}(4h+3)2

Problem 643

Problem 644

find + simplify f(x)=x2−6f(x)=x^{2}-6f(x)=x2−6

Problem 645

Determine if the equation x2−y=9 x^2 - y = 9 x2−y=9 defines a function.

Problem 646

12/16
If the blue graph is $f(x)=x^{2}$ then the red must be... $g(x)=x^{2}+5$ $g(x)=(x-5)^{2}$ $g(x)=(x+5)^{2}$ $g(x)=x^{2}-5$

Solve the equation. (Enter your answers as a comma-separated list.) $\begin{array}{l} x^{2}+13 x+36=0 \\ x=\square \end{array}$

(1 point) Which function has a maximum value? a. $f(x)=1.2(x+3)^{2}+1.5$ b. $f(x)=-3(x-12)^{2}+5$ c. $f(x)=2(x-15)^{2}-3$ (c.) $f(x)=(x-13)^{2}+12$

Short Answer
10. (3 points) Sketch the graph of $f(x)=-(x-4)^{2}+2$ , then state the domain and range of the function.

(2 points) Determine the equation that defines a quadratic function with $x$ -intercepts located at $(-9,0)$ and $(-2,0)$ and a $y$ -intercept of $(0,18)$ .

The sum of two distinct numbers is 39 and the product of the two numbers is 360 . Find the two numbers using a system of nonlinear equations. Enter your answers as a comma-separated list.
Answer: $\square$
Submit answer

Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms. Second-degree, with zeros of -6 and 2 , and goes to $-\infty$ as $x \rightarrow-\infty$ .
Answer

3. ( 3 points) Determine the equation that defines a quadratic function with $x$ -intercepts located at $(-9,0)$ and $(-2$ , 0 ) and a $y$ -intercept of $(0,18)$ .

$b^{2} - 13b + 42$

$m^{2} + m - 42$

Question Watch Video Show
Express $(x-12)^{2}$ as a trinomial in standard form. Answer Attempt 1 out of 2

$x^{2}-7 x-60$

Solve the equation using the quadratic formula.
1. $5 x^{2}+x-3=0$
2. $8 x^{2}+6 x+5=0$
3. $2 x^{2}-x-4=0$
4. $x^{2}+16 x+64=0$
5. $x^{2}-8 x+12=0$

Use the square root property to solve the quadratic equation. $4 x^{2}-8=0$

$\begin{array}{l}f(x)=(4-x)^{2} \\ f(11)=\square\end{array}$

$\begin{array}{l}f(x)=(1+x)^{2} \\ f(9)=\square\end{array}$

$\begin{array}{l}f(y)=y^{2}-10 y \\ f(s+2)=\end{array}$

Solve the equation $3 x^{2}+9 x+2=0$ to the nearest tenth.

Write an equation for the quadratic graphed below $x$ -intercepts: $(-1,0)$ and $(3,0) . y$ -intercept: $(0,-3)$ $y=$ $\square$

Answer the questions below about the quadratic function. $g(x)=x^{2}+8 x+17$
Does the function have a minimum or maximum value? Minimum Maximum
What is the function's minimum or maximum value? $\square$
Where does the minimum or maximum value occur? $x=$ $\square$

A ball is thrown vertically upward. After $t$ seconds, its height $h$ (in feet) is given by the function $h(t)=48 t-16 t^{2}$ . After how long will it reach its maximum height?
Do not round your answer.
Time: $\square$ seconds

$x^{2}+2 x-5=0$

A ball is thrown vertically upward. After $t$ seconds, its height $h$ (in feet) is given by the function $h(t)=112 t-16 t^{2}$ . After how long will it reach its maximum height?
Do not round your answer.
Time: $\square$ seconds

4 Use substitution to solve if $d=5.5$ $4.5+\left(d^{2}+45\right)-d$

Non-Calculator Q1. Express $4 x^{2}-12 x+14$ in the form $a(x+b)^{2}+c$

Solve for $u$ . $(u-3)^{2}=2 u^{2}-10 u-12$
If there is more than one solution, separate them with commas. $u=$ $\square$

1. Determine the value of $k$ such that $f(x)=2 x^{2}+8 x+11-k$ has only one zero.

2. find the zeres and verten for the function $f(x)=3 x^{2}+12 x-135$

Find the square. Simplify your answer. $(4 z-4)^{2}$

Determine, without graphing, whether the given quadratic function has a maximum value or a mir $f(x)=-4 x^{2}-16 x-9$
The quadratic function has a $\square$ value. minimum maximum

Find the square. Simplify your answer. $(4 h+3)^{2}$

find + simplify $f(x)=x^{2}-6$

Determine if the equation $x^2 - y = 9$ defines a function.

Find the equation of the axis of symmetry for the parabola $y=\frac{-3}{2} x^{2}-9 x-8$

$2 \cos ^{2} x-5 \cos x+2=0$

Use the quadratic formula to solve. Express your answer in simplest form. $-3 r^{2}+9 r+4=-5 r^{2}$

Use the quadratic formula to solve. Express your answer in simplest form. $6 w^{2}-7 w-3=0$

Use the quadratic formula to solve. Express your answer in simplest form $3 c^{2}+14 c-8=4 c$

Solve using the quadratic formula and find the zeros $f(x)=(x-1)\left(x^{2}-x+1\right)$

17. A soccer ball is kicked with an initial vertical velocity of $64 \mathrm{ft} / \mathrm{s}$ . The function $h(t)=-16 t^{2}+64$ models the height $h$ (in feet) of the soccer ball at time $t$ (in seconds). When does the soccer ball reach the ground?

Given the expression below, state the method that would be used to factor the expression. Then, factor it completely. $4 x^{2}-9$
Method: $\square$
Factored form: [Select] $\square$

The product of two numbers is 240 . The first number is 8 less than the second number. Which equation can be used to find $x$ , the lesser number? $x(x-8)=240$ $x(x+8)=240$ $x^{2}-8=240$ $x^{2}+8=240$

$x^{2}-4 \geqslant 0$

Graph the parabola. $y=3 x^{2}-12 x+5$
Plot five points on the parabola: the vertex, two points to the left of the vertex, and two points to the right of the vertex. Then click on the graph-a-function button.

48. $y=\frac{1}{2}(x+4)(x-2)$

8.2 Solve the following inequalities analytically, using sign diagrams. Verify your answer graphically (a) $x^{2}-2 \leq 2 x$ (b) $12 x-4 \geq 9 x^{2}$

$f(x)=-2 x^{2}-8 x-4$
Does the function have a minimum or maximum value? Minimum Maximum
What is the function's minimum or maximum value? $\square$ Where does the minimum or maximum value occur? $x=-12$

$\begin{array}{l} \text { 2. } y=x^{2}-6 x+5 \\ y=12 \\ \begin{array}{l} 12=x^{2}-6 x+5 \\ -12 \quad-12 \end{array} \\ x^{2}-6 x-7=0 \end{array}$

Evaluate the expression when $c=3$ . $c^{2}-5 c+2$

uation $(n-2)^{2}=49$ reasoning.