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

Question

shansha1 · Answer

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)