Answer:
2x²-2x-24
Step-by-step explanation:
Something has roots of 4 and -3 we can write
(x-4)(x+3)
We then attach a constant, a that will ensure that it passes through the correct point
a(x-4)(x+3)
now plug in the numbers and solve for a
a(3-4)(3+3)= -12
a(-1)(6)= -12
-6a= -12
a=2
So we have
2(x-4)(x+3)
and now it's just a matter of mulitplying/simplifying things
(x-4)(x+3)= x²-x-12
2(x²-x-12)= 2x²-2x-24
Answer:
y = 2x² - 2x - 24
Step-by-step explanation:
Given a root x = a then the factor is (x - a )
Given roots are x = 4 and x = - 3 , the corresponding factors are
(x - 4) and (x - (- 3)) , that is (x - 4) and (x + 3)
The quadratic is then the product of the factors
y = a(x - 4)(x + 3) ← a is a multiplier
To find a substitute (3, - 12) into the equation
- 12 = a(- 1)(6) = - 6a ( divide both sides by - 6 )
2 = a
y = 2(x - 4)(x + 3) ← expand factors using FOIL
= 2(x² - x - 12) ← distribute
y = 2x² - 2x - 24
