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Q55.

Expert-verifiedFound in: Page 416

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

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

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

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

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

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