Question

Determine the equation with roots -4 and 2 and goes through (6, 20)

Answer 1

y =
`(1)/(2)` x² + x - 4

Explanation:

Given roots x = a and x = b, then the factors are

(x - a) and (x - b)

The function is then the product of the factors

y = a(x - a)(x - b) ← where a is a multiplier

Given roots are x = - 4 and x = 2 then the factors are

(x - (- 4)) and (x - 2), that is (x + 4) and (x - 2), thus

y = a(x + 4)(x - 2)

To find a substitute (6, 20) into the function

20 = a(6 + 4)(6 - 2) = a(10)(4) = 40a ( divide both sides by 40 ), thus

a =
`(20)/(40)` =
`(1)/(2)`

y =
`(1)/(2)` (x + 4)(x - 2) ← expand factors

=
`(1)/(2)` (x² + 2x - 8) ← distribute

y =
`(1)/(2)` x² + x - 4