# How do you write the equation of the parabola in vertex form given vertex (3, -2), point (2, 3)?

Sep 6, 2017

$y = 5 {\left(x - 3\right)}^{2} - 2$

#### 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.

$\text{here } \left(h , k\right) = \left(3 , - 2\right)$

$\Rightarrow y = a {\left(x - 3\right)}^{2} - 2$

$\text{to find a substitute "(2,3)" into the equation}$

$3 = a - 2 \Rightarrow a = 5$

$\Rightarrow y = 5 {\left(x - 3\right)}^{2} - 2 \leftarrow \textcolor{red}{\text{ in vertex form}}$
graph{5(x-3)^2-2 [-10, 10, -5, 5]}