# How do you write the equation of the parabola in vertex form given Vertex: (4, 4); point: (0, 0)?

Dec 21, 2017

$y = - \frac{1}{4} {\left(x - 4\right)}^{2} + 4$

#### Explanation:

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

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

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

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

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

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

$0 = 16 a + 4 \Rightarrow a = - \frac{4}{16} = - \frac{1}{4}$

$\Rightarrow y = - \frac{1}{4} {\left(x - 4\right)}^{2} + 4 \leftarrow \textcolor{red}{\text{in vertex form}}$
graph{(y+1/4x^2-2x)((x-4)^2+(y-4)^2-0.04)=0 [-10, 10, -5, 5]}