Question

The parabola has a vertex of (1,-16) and y intercept of (0,-15) that crosses the x axis in two places. one x intercept is (5,0) what is the other x intercept

Answer 1

Vertex form is:

y = a(x - 1)^2 - 16  where a is a cosntant

at y intercept we have

-15 = a^2 - 16
a^2 = 1

so equation of the parabola is y = (x-1)^2 - 16

the equation of symmetry is x = 1  and both roots are same distance either side of the point (1,0) so the other x-intercept  is  1 - 4 =   (-3,0)