Question

The vertex of a parabola is (-2, -20), and its y-intercept is (0, -12). The equation of the parabola is y = __ x2 +__x + __

Answer 1

the vertex form of a parabola is

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

so here we have

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

when x = 0 y = -12 (from y-intercept) so:-

-12 = 4a - 20

4a = 8
a = 2

so required equation is y = 2(x + 2)^2 - 20

convert to standard form

y = 2x^2 + 8x + 8 - 20

y = 2x^2 + 8x - 12