# How do you write a quadratic function in vertex form whose graph has the vertex (2,-4) and point (0,0)?

##### 1 Answer
Aug 14, 2017

$y = {\left(x - 2\right)}^{2} - 4$

#### 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.

$\text{here vertex } = \left(2 , - 4\right) = \left(h , k\right)$

$\Rightarrow y = a {\left(x - 2\right)}^{2} - 4$

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

$0 = 4 a - 4 \Rightarrow a = 1$

$\Rightarrow y = {\left(x - 2\right)}^{2} - 4 \leftarrow \textcolor{red}{\text{ in vertex form}}$
graph{(x-2)^2-4 [-10, 10, -5, 5]}