Question

Write the equation of a parabola in factored form if the x-intercepts are (3,0) and (-5,0) with a maximum point at ( -1,8)

Answer 1

y = -
`(1)/(2)` (x - 3)(x + 5)

Explanation:

Given the x- intercepts are x = 3 and x = - 5 then the corresponding factors are

(x - 3) and (x + 5)

The equation is the the product of the factors, that is

y = a(x - 3)(x + 5) ← a is a multiplier

To find a substitute (- 1, 8) into the equation

8 = a(- 1 - 3)(- 1 + 5) = a(- 4)(4) = - 16a ( divide both sides by - 16 )

-
`(1)/(2)` = a

Then

y = -
`(1)/(2)` (x - 3)(x + 5) ← in factored form