Question

find the x-intercepts of the parabola with vertex(-2,-8)and y-intercept(0,4).

Answer 1

An equation of the parabola is y = A(x-h)2+k, where (h,k) is the vertex.

So, y = A(x+2)2 - 8

Since (0,4) is on the graph, 4 = 4A-8

4A = 12

A = 3

So, y = 3(x+2)2-8

To locate the x-intercepts, set y = 0 and solve for x:

0 = 3(x+2)2-8

3(x+2)2 = 8

x+2 = ±√(8/3)

x = -2 ± √(8/3)

The x-intercepts are (2+√(8/3),0) and (2-√(8/3),0)