Answer:
[tex]\large\boxed{y=\dfrac{1}{3}x^2=\dfrac{x^2}{3}}[/tex]
Step-by-step explanation:
The vertex form of na equation of a parabola:
[tex]y=a(x-h)^2+k[/tex]
(h, k) - vertex
We have a vertex in (0, 0). Therefore h = 0, k = 0.
The equation has form:
[tex]y=a(x-0)^2+0=ax^2[/tex]
From the graph we have the point (3, 3).
Put the coordinates of the point to the equation:
[tex]3=a(3^2)[/tex]
[tex]3=9a[/tex] divide both sides by 9
[tex]\dfrac{3}{9}=\dfrac{9a}{9}\\\\\dfrac{3:3}{9:3}=a\to a=\dfrac{1}{3}[/tex]
