# What is the equation of the parabola that has a vertex at  (2, -5)  and passes through point  (-8,-7) ?

##### 1 Answer
Oct 5, 2017

$y = - \frac{1}{50} {\left(x - 2\right)}^{2} - 5$

#### Explanation:

$\text{the equation of a parabola in "color(blue)"vertex form}$ is.

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

$\text{where "(h,k)" are the coordinates of the vertex and a is}$
$\text{a multiplier}$

$\text{here } \left(h , k\right) = \left(2 , - 5\right)$

$\Rightarrow y = a {\left(x - 2\right)}^{2} - 5$

$\text{to find a substitute "(-8,-7)" into the equation}$

$- 7 = 100 a - 5$

$\Rightarrow a = - \frac{1}{50}$

$\Rightarrow y = - \frac{1}{50} {\left(x - 2\right)}^{2} - 5 \leftarrow \textcolor{red}{\text{ in vertex form}}$

$\text{distributing and collecting like terms}$

$y = - \frac{1}{50} {x}^{2} + \frac{2}{25} x - \frac{127}{25} \leftarrow \textcolor{red}{\text{ in standard form}}$