# How do you find the standard form of an equation with a given Vertex: (0,0) and Point on Parabola: (3,6)?

Jun 20, 2018

$y = \frac{2}{3} {x}^{2}$

#### Explanation:

$\text{since the vertex is at the origin then the standard form is}$

•color(white)(x)y=ax^2

$\text{to find a substitute "(3,6)" into the equation}$

$6 = 9 a \Rightarrow a = \frac{6}{9} = \frac{2}{3}$

$\text{required equation is } y = \frac{2}{3} {x}^{2}$
graph{(y-2/3x^2)((x-3)^2+(y-6)^2-0.04)=0 [-15.8, 15.81, -7.9, 7.9]}