Question

Find the quadratic function that has a vertex at (−3,−1) and goes through the point (0,8).

Answer 1

A quadratic function is a parabola of the form:

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

We know the vertex so h=-3 and k=-1, therefore:

y+1=a(x+3)².

And we know the parabola passes through (0,8) so:

8+1=a(0+3)²=9a, so 9a=9 and a=1.

The equation is y+1=(x+3)²=x²+6x+9,

y=x²+6x+9-1=x²+6x+8.