Chapter 5: Q. 10 (page 494)

Fill in the blanks to complete each of the following theorem statements:
Every quadratic function $x^{2} + b x + c$ can be rewritten in the form $x^{2} + b x + c = {(x - k)}^{2} + C$ , where $k =_$ and $C =_$ .

Short Answer

Expert verified

Every quadratic function $x^{2} + b x + c$ can be rewritten in the form $x^{2} + b x + c = {(x - k)}^{2} + C$ , where $k = - \frac{b}{2}$ and $C = c - \frac{b^{2}}{4}$ .

Step by step solution

Step 1. Given information

Every quadratic function $x^{2} + b x + c$ can be rewritten in the form $x^{2} + b x + c = {(x - k)}^{2} + C$ , where $k =_____$ and $C =_____$ .

Step 2. Filling in the blanks to complete the theorem statements

Every quadratic function $x^{2} + b x + c$ can be rewritten in the form $x^{2} + b x + c = {(x - k)}^{2} + C$ , where $k = - \frac{b}{2}$ and $C = c - \frac{b^{2}}{4}$ .

By completing the square method, the above form and the relationships between the terms are obtained.

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Fill in the blanks to complete each of the following theorem statements:
Every quadratic function $x^{2} + b x + c$ can be rewritten in the form $x^{2} + b x + c = {(x - k)}^{2} + C$ , where $k =_$ and $C =_$ .

Short Answer

Step by step solution

Step 1. Given information

Step 2. Filling in the blanks to complete the theorem statements

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Fill in the blanks to complete each of the following theorem statements: Every quadratic function x2+bx+ccan be rewritten in the form x2+bx+c=x-k2+C, where k=_____and C=_____.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Filling in the blanks to complete the theorem statements

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Calculus

Probability and Statistics

Mechanics Maths

Pure Maths

Statistics

Study anywhere. Anytime. Across all devices.

Fill in the blanks to complete each of the following theorem statements:
Every quadratic function $x^{2} + b x + c$ can be rewritten in the form $x^{2} + b x + c = {(x - k)}^{2} + C$ , where $k =_$ and $C =_$ .