# How do you write y = (x-2)^2 - 16 in standard form?

Jan 4, 2017

${x}^{2} - 4 x - 12$

#### Explanation:

The standard form of a $\textcolor{b l u e}{\text{quadratic function}}$ is

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = a {x}^{2} + b x + c} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

To obtain $y = {\left(x - 2\right)}^{2} - 16 \text{ in this form}$ expand the brackets and simplify.

$y = {\left(x - 2\right)}^{2} - 16 = \left(\textcolor{red}{x - 2}\right) \left(x - 2\right) - 16$

$= \textcolor{red}{x} \left(x - 2\right) \textcolor{red}{- 2} \left(x - 2\right) - 16$

$= {x}^{2} - 2 x - 2 x + 4 - 16$

collecting like terms.

$\Rightarrow y = {x}^{2} - 4 x - 12 \leftarrow \text{ in standard form}$