Question

HELP NOW

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

y = 0.7(x^2 - 64x - 576)

Average rate of change = -49.

Explanation:

As the x intercepts are -8 and 72 we can write the equation

y = a(x + 8)(x - 72) where a is some constant to be found.

As it passes through point (62, -490) we have, substituting:

-490 = a(62+8)(62-72)

-490 = - 700a

a = 0.7

So the equation of the parabola

y = 0.7(x + 8)(x - 72) or

y = 0.7(x^2 - 64x - 576).

Average rate of change between x = -8 and x = 2

= [0.7(2+ 8)(2 - 72) - 0.7(-8+8)(-8-72)] / (2 - -8)

= -490 - 0 /10

= -49