Math / Algebra

Question(Vocabulary and Concepts) Fill in the blanks to make each statement true.
1. If $a, b$ , and $c$ are real numbers, and $a \neq 0$ , then the general quadratic equation is $\qquad$ ・
2. The formula $x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$ is called the $\qquad$ formula.
3. The expression $\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$ can be read as "The $\qquad$ of $b$ , plus $\qquad$ the $\qquad$ root of $b$ $\qquad$ minus 4 $\qquad$ $a$ times $c$ , all $\qquad$ 2a."
4. To use the quadratic formula, we begin by writing the equation in . $\qquad$
5. Although the quadratic formula can be used to solve $x^{2}-3 x=0$ , the $\qquad$ method is easier.

Studdy Solution

STEP 1

1. The problem involves understanding and applying the terminology related to quadratic equations and their solutions.
2. The quadratic equation is generally written in the form $ax^2 + bx + c = 0$ .
3. The quadratic formula is used to solve quadratic equations.
4. Understanding the vocabulary of the quadratic formula and recognizing simpler methods for specific cases is required.

STEP 2

1. Identify the general form of a quadratic equation.
2. Recognize and name the formula for solving a general quadratic equation.
3. Explain the reading of each part of the quadratic formula.
4. Describe the initial step in using the quadratic formula.
5. Identify an easier method for solving specific quadratic equations.

STEP 3

Identify the general form of a quadratic equation.
If $a, b$ , and $c$ are real numbers, and $a \neq 0$ , then the general quadratic equation is: $ax^2 + bx + c = 0$

STEP 4

Recognize the formula for solving a general quadratic equation.
The formula $x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$ is called the: $\text{quadratic formula}$

STEP 5

Explain the reading of each part of the quadratic formula.
The expression $\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$ can be read as: $\text{"The opposite of } b, \text{ plus or minus the square root of } b^2 \text{ minus 4 times } a \text{ times } c, \text{ all divided by } 2a."$

STEP 6

Describe the initial step in using the quadratic formula.
To use the quadratic formula, we begin by writing the equation in: $\text{standard form, } ax^2 + bx + c = 0$

STEP 7

Identify an easier method for solving specific quadratic equations.
Although the quadratic formula can be used to solve $x^2 - 3x = 0$ , the: $\text{factoring method}$ is easier.

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Studdy Solution

STEP 1

STEP 2

STEP 3

Identify the general form of a quadratic equation.
If $a, b$ , and $c$ are real numbers, and $a \neq 0$ , then the general quadratic equation is: $ax^2 + bx + c = 0$

STEP 4

Recognize the formula for solving a general quadratic equation.
The formula $x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$ is called the: $\text{quadratic formula}$

STEP 5

Explain the reading of each part of the quadratic formula.
The expression $\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$ can be read as: $\text{"The opposite of } b, \text{ plus or minus the square root of } b^2 \text{ minus 4 times } a \text{ times } c, \text{ all divided by } 2a."$

STEP 6

Describe the initial step in using the quadratic formula.
To use the quadratic formula, we begin by writing the equation in: $\text{standard form, } ax^2 + bx + c = 0$

STEP 7

Identify an easier method for solving specific quadratic equations.
Although the quadratic formula can be used to solve $x^2 - 3x = 0$ , the: $\text{factoring method}$ is easier.

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Studdy Solution

STEP 1

STEP 2

STEP 3

Identify the general form of a quadratic equation.If a,ba, ba,b, and ccc are real numbers, and a≠0a \neq 0a=0, then the general quadratic equation is: ax2+bx+c=0 ax^2 + bx + c = 0 ax2+bx+c=0

STEP 4

Recognize the formula for solving a general quadratic equation.The formula x=−b±b2−4ac2ax=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}x=2a−b±b2−4ac​​ is called the: quadratic formula \text{quadratic formula} quadratic formula

STEP 5

STEP 6

Describe the initial step in using the quadratic formula.To use the quadratic formula, we begin by writing the equation in: standard form, ax2+bx+c=0 \text{standard form, } ax^2 + bx + c = 0 standard form, ax2+bx+c=0

STEP 7

Identify an easier method for solving specific quadratic equations.Although the quadratic formula can be used to solve x2−3x=0x^2 - 3x = 0x2−3x=0, the: factoring method \text{factoring method} factoring method is easier.

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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.

Identify the general form of a quadratic equation.
If $a, b$ , and $c$ are real numbers, and $a \neq 0$ , then the general quadratic equation is: $ax^2 + bx + c = 0$

Recognize the formula for solving a general quadratic equation.
The formula $x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$ is called the: $\text{quadratic formula}$

Describe the initial step in using the quadratic formula.
To use the quadratic formula, we begin by writing the equation in: $\text{standard form, } ax^2 + bx + c = 0$

Identify an easier method for solving specific quadratic equations.
Although the quadratic formula can be used to solve $x^2 - 3x = 0$ , the: $\text{factoring method}$ is easier.