Answer:
[tex]\large\boxed{y=-\dfrac{4}{27}(x-3)^2}[/tex]
Step-by-step explanation:
The vertex form of na equation of a parabola:
[tex]y=a(x-h)^2+k[/tex]
We have the vertex (3, 0). Substitute:
[tex]y=a(x-3)^2+0=a(x-3)^2[/tex]
A parabola passes through (12, -12). Put the coordinates of the point to the equation and solve for a:
[tex]-12=a(12-3)^2[/tex]
[tex]-12=a(9)^2[/tex]
[tex]-12=81a[/tex] divide both sides by 81
[tex]-\dfrac{12}{81}=a\\\\a=-\dfrac{4}{27}[/tex]
Finally:
[tex]y=-\dfrac{4}{27}(x-3)^2[/tex]
