Math / Algebra

QuestionGraph the functions on the same coordinate plane. $\begin{array}{l} f(x)=-2 x \\ g(x)=x^{2}-3 \end{array}$
What are the solutions to the equation $f(x)=g(x)$ ? Select each correct answer. There are two.
Select 2 correct answer(s)
1 -3 -2 0

Studdy Solution

STEP 1

What is this asking? We need to draw two functions, $f(x)$ and $g(x)$ , on the same graph and find the \x-values where they intersect! Watch out! Make sure to graph accurately to find the correct intersection points.
Don't mix up $f(x)$ and $g(x)$ !

STEP 2

1. Define the functions
2. Find the intersection points
3. Solve for x

STEP 3

Alright, let's define our functions!
We have $f(x) = -2x$ , which is a straight line, and $g(x) = x^2 - 3$ , which is a parabola.
Exciting!

STEP 4

To find where these two graphs intersect, we need to find the \x values where $f(x)$ equals $g(x)$ .
That means we're solving for \x when $-2x = x^2 - 3$ .

STEP 5

Let's rewrite the equation to make it easier to solve: $0 = x^2 + 2x - 3$ .
Now, we can factor this quadratic equation!
We're looking for two numbers that multiply to $-3$ and add up to $2$ .

STEP 6

Those numbers are $3$ and $-1$ .
So, our factored equation is $(x + 3)(x - 1) = 0$ .

STEP 7

Now, we set each factor equal to zero and solve for \x.
If $x + 3 = 0$ , then $x = -3$ .
If $x - 1 = 0$ , then $x = 1$ .
Boom!

STEP 8

The solutions to the equation $f(x) = g(x)$ are \x = -3 and \x = 1.
So the correct answers are $-3$ and $1$ .

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QuestionGraph the functions on the same coordinate plane. $\begin{array}{l} f(x)=-2 x \\ g(x)=x^{2}-3 \end{array}$
What are the solutions to the equation $f(x)=g(x)$ ? Select each correct answer. There are two.
Select 2 correct answer(s)
1 -3 -2 0

Studdy Solution

STEP 1

What is this asking? We need to draw two functions, $f(x)$ and $g(x)$ , on the same graph and find the \x-values where they intersect! Watch out! Make sure to graph accurately to find the correct intersection points.
Don't mix up $f(x)$ and $g(x)$ !

STEP 2

1. Define the functions
2. Find the intersection points
3. Solve for x

STEP 3

Alright, let's define our functions!
We have $f(x) = -2x$ , which is a straight line, and $g(x) = x^2 - 3$ , which is a parabola.
Exciting!

STEP 4

To find where these two graphs intersect, we need to find the \x values where $f(x)$ equals $g(x)$ .
That means we're solving for \x when $-2x = x^2 - 3$ .

STEP 5

Let's rewrite the equation to make it easier to solve: $0 = x^2 + 2x - 3$ .
Now, we can factor this quadratic equation!
We're looking for two numbers that multiply to $-3$ and add up to $2$ .

STEP 6

Those numbers are $3$ and $-1$ .
So, our factored equation is $(x + 3)(x - 1) = 0$ .

STEP 7

Now, we set each factor equal to zero and solve for \x.
If $x + 3 = 0$ , then $x = -3$ .
If $x - 1 = 0$ , then $x = 1$ .
Boom!

STEP 8

The solutions to the equation $f(x) = g(x)$ are \x = -3 and \x = 1.
So the correct answers are $-3$ and $1$ .

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Studdy Solution

STEP 1

What is this asking? We need to draw two functions, f(x)f(x)f(x) and g(x)g(x)g(x), on the same graph and find the \x-values where they intersect! Watch out! Make sure to graph accurately to find the correct intersection points.Don't mix up f(x)f(x)f(x) and g(x)g(x)g(x)!

STEP 2

1. Define the functions2. Find the intersection points3. Solve for x

STEP 3

Alright, let's **define** our functions!We have f(x)=−2xf(x) = -2xf(x)=−2x, which is a straight line, and g(x)=x2−3g(x) = x^2 - 3g(x)=x2−3, which is a parabola.Exciting!

STEP 4

To find where these two graphs **intersect**, we need to find the \x values where f(x)f(x)f(x) equals g(x)g(x)g(x).That means we're solving for \x when −2x=x2−3-2x = x^2 - 3−2x=x2−3.

STEP 5

Let's **rewrite** the equation to make it easier to solve: 0=x2+2x−30 = x^2 + 2x - 30=x2+2x−3.Now, we can **factor** this quadratic equation!We're looking for two numbers that multiply to −3-3−3 and add up to 222.

STEP 6

Those numbers are 333 and −1-1−1.So, our factored equation is (x+3)(x−1)=0(x + 3)(x - 1) = 0(x+3)(x−1)=0.

STEP 7

Now, we set each factor equal to zero and **solve** for \x.If x+3=0x + 3 = 0x+3=0, then x=−3x = -3x=−3.If x−1=0x - 1 = 0x−1=0, then x=1x = 1x=1.Boom!

STEP 8

The solutions to the equation f(x)=g(x)f(x) = g(x)f(x)=g(x) are \x = -3 and \x = 1.So the correct answers are −3-3−3 and 111.

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

What is this asking? We need to draw two functions, $f(x)$ and $g(x)$ , on the same graph and find the \x-values where they intersect! Watch out! Make sure to graph accurately to find the correct intersection points.
Don't mix up $f(x)$ and $g(x)$ !

1. Define the functions
2. Find the intersection points
3. Solve for x

Alright, let's define our functions!
We have $f(x) = -2x$ , which is a straight line, and $g(x) = x^2 - 3$ , which is a parabola.
Exciting!

To find where these two graphs intersect, we need to find the \x values where $f(x)$ equals $g(x)$ .
That means we're solving for \x when $-2x = x^2 - 3$ .

Let's rewrite the equation to make it easier to solve: $0 = x^2 + 2x - 3$ .
Now, we can factor this quadratic equation!
We're looking for two numbers that multiply to $-3$ and add up to $2$ .

Those numbers are $3$ and $-1$ .
So, our factored equation is $(x + 3)(x - 1) = 0$ .

Now, we set each factor equal to zero and solve for \x.
If $x + 3 = 0$ , then $x = -3$ .
If $x - 1 = 0$ , then $x = 1$ .
Boom!

The solutions to the equation $f(x) = g(x)$ are \x = -3 and \x = 1.
So the correct answers are $-3$ and $1$ .