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Q55.

Expert-verified

Algebra 2

Found in: Page 416

Book edition Middle English Edition

Author(s) Carter

Pages 804 pages

ISBN 9780079039903

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Short Answer

Write the equation $y = x^{2} - 4 x + 1$ in the form $y = a {(x - h)}^{2} + k$ .

The required form of the equation in $y = a {(x - h)}^{2} + k$ is $y = {(x - 2)}^{2} - 3$ where $a = 1, h = 2 and k = - 3$ .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Write down the given information.

The given equation is $y = x^{2} - 4 x + 1$ .

Step 2. Calculation.

The given equation $y = x^{2} - 4 x + 1$ is converted to $y = a {(x - h)}^{2} + k$ form as:

\begin{matrix} y = x^{2} - 4 x + 1 \\ = x^{2} - 4 x + 1 + {(- 2)}^{2} - {(- 2)}^{2} .... (\begin{array}{l} Add and subtract \\ square of {(- 2)}^{2} \end{array}) \\ = (x^{2} - 4 x + {(- 2)}^{2}) + (1 - {(- 2)}^{2}) \\ = {(x - 2)}^{2} - 3 \end{matrix}

Here $a = 1, h = 2 and k = - 3$ .

Step 3. Conclusion.

The required form of the given equation is $y = {(x - 2)}^{2} - 3$ where $a = 1, h = 2 and k = - 3$ .

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