# How do you write the standard form of the equation of the parabola that has the indicated vertex and whose graph passes through the point Vertex (-2,5); Point ( 0,9)?

Jul 20, 2018

$y = {x}^{2} + 4 x + 9$

#### Explanation:

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

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

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

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

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

$\text{to find a substitute "(0,9)" into the equation}$

$9 = 4 a + 5 \Rightarrow 4 a = 4 \Rightarrow a = 1$

$y = {\left(x + 2\right)}^{2} + 5 \leftarrow \textcolor{red}{\text{in vertex form}}$

$\textcolor{w h i t e}{y} = {x}^{2} + 4 x + 4 + 5$

$y = {x}^{2} + 4 x + 9 \leftarrow \textcolor{red}{\text{in standard form}}$