Write an equation of the parabola that passes through the point (62,−490) and has x-intercepts −8 and 72. Then find the average rate of change from x=−8 to x=2.

Question

Write an equation of the parabola that passes through the point (62,−490) and has x-intercepts −8 and 72. Then find the average rate of change from x=−8 to x=2.

Answer 1

Hi Jordan,

The x-intercepts are the values of x that make y equal to 0. So the equation in factored form is

y = A(x+8)(x-2)

Plug in the point (62,-490) for (x,y) to determine the value of A.

The average rate of change from x = -8 to x = 2 is just the slope of the line connecting the 2 points on the parabola. Since they have the same y value this will be a very easy calculation.