[tex]y = \frac{1}{3} {x}^{2} - 3[/tex]
Step-by-step explanation:
The general vertex form of the equation is
[tex]y = a {(x - h)}^{2} + k[/tex]
where (h, k) are the coordinates of the vertex and a is a constant. In your case, the vertex is located at (0, -3) so your equation becomes
[tex]y = a {x}^{2} - 3[/tex]
To find a, substitute the point (3, 0) into the equation
0 = a(3)^2 - 3 ---> a = 1/3
Therefore, the equation has the form
[tex]y = \frac{1}{3} {x}^{2} - 3[/tex]
