# How do you write the function in standard form y=-(x-5)^2+11?

Aug 25, 2016

$- {x}^{2} + 10 x - 14$

#### Explanation:

The function $y = - {\left(x - 5\right)}^{2} + 11$ is in $\textcolor{b l u e}{\text{vertex form}}$

To write it in $\textcolor{b l u e}{\text{standard form}}$ distribute $- {\left(x - 5\right)}^{2}$

distribute using, for example, the FOIL method.

$\Rightarrow - {\left(x - 5\right)}^{2} = - \left({x}^{2} - 10 x + 25\right) = - {x}^{2} + 10 x - 25$

$\Rightarrow y = - {x}^{2} + 10 x - 25 + 11 = - {x}^{2} + 10 x - 14$