Answer:
[tex]\large\boxed{y=2x^2+4}[/tex]
Step-by-step explanation:
The vertex form of a parabola:
[tex]y=a(x-h)^2+k[/tex]
(h, k) - vertex
We have the vertex at (0, 4) → h = 0 and k = 4.
Substitute:
[tex]y=a(x-0)^2+4=ax^2+4[/tex]
The point (-1, 6) is on the parabola. Put the coordinates of the point to the equation:
[tex]6=a(-1)^2+4[/tex] subtract 4 from both sides
[tex]2=a\to a=2[/tex]
Finally:
[tex]y=2x^2+4[/tex]
