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Q55.

Expert-verified
Found in: Page 416

Algebra 2

Book edition Middle English Edition
Author(s) Carter
Pages 804 pages
ISBN 9780079039903

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

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

See the step by step solution

Step 1. Write down the given information.

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

Step 2. Calculation.

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

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

Here $a=1,h=2\text{and}k=-3$.

Step 3. Conclusion.

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