Answer:
[tex]y=\frac{3}{4}x^2[/tex]
Step-by-step explanation:
Hi there!
Because we're given the vertex of the parabola, we can determine its equation in vertex form:
[tex]y=a(x-h)^2+k[/tex] where the vertex is [tex](h,k)[/tex]
Plug in the vertex (0,0)
[tex]y=a(x-0)^2+0\\y=a(x)^2\\y=a(x-0)^2+0\\y=ax^2[/tex]
Now, we must solve for a. Plug in the given point (-2,3) and solve for a:
[tex]3=a(-2)^2\\3=4a\\\frac{3}{4} =a[/tex]
Therefore, the value of a is [tex]\frac{3}{4}[/tex]. Plug this back into [tex]y=ax^2[/tex]:
[tex]y=\frac{3}{4}x^2[/tex]
I hope this helps!
