Answer:
y = [tex]\frac{1}{2}[/tex] x² + x - 4
Step-by-step 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 = [tex]\frac{20}{40}[/tex] = [tex]\frac{1}{2}[/tex]
y = [tex]\frac{1}{2}[/tex] (x + 4)(x - 2) ← expand factors
= [tex]\frac{1}{2}[/tex] (x² + 2x - 8) ← distribute
y = [tex]\frac{1}{2}[/tex] x² + x - 4
