Answer:
a = 2 , b = 2 , c = - 12
Explanation:
given the zeros of f(x) are say x = a and x = b , then the corresponding factors are (x - a) and (x - b)
the function is then the product of the factors , that is
f(x) = p(x - a)(x - b) ← p is a multiplier
from the graph the zeros are x = - 3 and x = 2 , then factors are
(x - (- 3) ) and (x - 2) , that is (x + 3) and (x - 2) , then
f(x) = p(x + 3)(x - 2)
to find p substitute any other point lying on the graph into f(x)
using the point (1, - 8 )
- 8 = p(1 + 3)(1 - 2)
- 8 = p(4)(- 1) = - 4p ( divide both sides by - 4 )
2 = p
f(x) = 2(x + 3)(x - 2) ← expand factors using FOIL
= 2(x² + x - 6) ← distribute parenthesis by 2
f(x) = 2x² + 2x - 12 ← in the form ax² + bx + c , and by comparison
a = 2 , b = 2 , c = - 12