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

An equation is  y=__?

The average rate of change is __?

Answer 1

Since the x intercepts are known, the factored form of a parabola is useful

f(x) = A (x + 2) (x - 18) for some value of A. But f(3) = -30 so A can be be determined.

With some algebra, it is found that A = 2/5

The final form is f(x) = (2/5) (x + 2) ( x - 18)

The average rate of change from x = -2 to 8 is [f(8) - f(-2) ] /( 8 - (-2) ) = -4