Write an equation of the parabola that passes through the point (3,−30) and has x-intercepts −2 and 18. Then find the average rate of change from x=−2 to x=8.

Question

Write an equation of the parabola that passes through the point (3,−30) and has x-intercepts −2 and 18. Then find the average rate of change from x=−2 to x=8.

Answer 1

-2 and 18 are solutions ---> (x+2)(x-18) are factors

y = k(x+2)(x-18)

-30 = k(1)(-15)

k = 2

y = 2(x+2)(x-18) = f(x)

f(-2) = 0

f(8) = 2(10)(-10) = -200

(-200 - 0) / (8- -2) =

-200/10 =

-20

Answer 2

f(x) = a(x - h)² + k

-30 = a(3 - h)² + k

0 = a(-2 - h)² + k

0 = a(8 - h)² + k

Solve the system for a, h, and k.