# How do you write y=-5/4(x+4)^2+15 in standard form?

Apr 12, 2017

$y = - \frac{5}{4} {x}^{2} - 10 x - 5$

#### Explanation:

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

color(red)(bar(ul(|color(white)(2/2)color(black)(y=ax^2+bx+c;a!=0)color(white)(2/2)|)))

$\text{Rearrange " y=-5/4(x+4)^2+15" into this form}$

$\text{Expand " (x+4)^2" using FOIL method}$

$\Rightarrow y = - \frac{5}{4} \left({x}^{2} + 8 x + 16\right) + 15$

$\textcolor{w h i t e}{\Rightarrow y} = - \frac{5}{4} {x}^{2} - 10 x - 20 + 15 \leftarrow \text{ distributing}$

$\Rightarrow y = - \frac{5}{4} {x}^{2} - 10 x - 5 \leftarrow \textcolor{red}{\text{ in standard form}}$