Question

The vertex of a parabola is (-2, -20), and its y-intercept is (0, -12).

Answer 1

Vertex for is

y = a(x - h)^2 + k  where (h,k) is the vertex.

so we have

y = a(x - (-2)^2 - 20
y = a(x + 2)^2 - 20

y intercept is (0,-12) so:-

-12 =  a(2)^2 - 20
4a = 8
a = 2

y = 2(x + 2)^2 - 20    is the parabola in vertex form  Convert to standard form:-

y = 2(x^2 + 4x + 4) - 20
y = 2x^2 + 8x -12  is the answer