Question

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

Answer 1

Part 1

The equation is
`y=a(x+8)(x-72)`.

Using the point
`(62, -490)` to solve for
`a`,

`-490=a(62+8)(62-72) \implies a=(7)/(10)\\\\\therefore \boxed{y=(7)/(10)(x+8)(x-72)}`

Part 2

When
`x=-8`,
`y=0`.

When
`x=2`,
`y=-490`.

So, the average rate of change is
`(-490-0)/(2-(-8))=\boxed{-49}`