How do i do this? Please help.
Find a quadratic function for each parabola described.
maximum value:6 x intercept -2 and 4

Question

How do i do this? Please help.
Find a quadratic function for each parabola described.
maximum value:6 x intercept -2 and 4

agent0smith · Answer

Since the x intercepts are -2 and 4, the axis of symmetry must be x=1 (since it has to be halfway between the roots. The max value is 6, so the vertex of the parabola is (1, 6) since the max value has to be where the axis of symmetry is. We can write it in vertex form:

$$y= a(x-h)^2+k$$where (h, k) is the vertex, so...$$y= a(x-1)^2+6$$ now just solve for a, by entering either of the x-intercepts, since y=0 at the x-intercepts:
$$0= a(4-1)^2+6$$ you could also enter -2 as x.