# How do you write the equation of the parabola in vertex form given vertex:(0,5) point:(3,8)?

Aug 17, 2017

$y = \frac{1}{3} {x}^{2} + 5$

#### Explanation:

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

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = a {\left(x - h\right)}^{2} + k} \textcolor{w h i t e}{\frac{2}{2}} |}}}$
where ( h , k ) are the coordinates of the vertex and a is a constant.

$\text{here } \left(h , k\right) = \left(0 , 5\right)$

$\Rightarrow y = a {\left(x - 0\right)}^{2} + 5$

$\text{to find a substitute "(3,8)" into the equation}$

$8 = 9 a + 5 \Rightarrow a = \frac{1}{3}$

$\Rightarrow y = \frac{1}{3} {x}^{2} + 5 \leftarrow \textcolor{red}{\text{ in vertex form}}$