Question

Write the equation of the graph shown below in factored form.

A. f(x) = (x − 2)2(x + 1)(x − 4)
B. f(x) = (x + 2)2(x − 1)(x + 4)
C. f(x) = (x + 2)2(x + 1)(x + 4)
D. f(x) = (x − 2)2(x − 1)(x − 4)

Answer 1

C

Explanation:

given x = a is a solution of f(x) then (x - a) is a factor

here the solutions, where the graph crosses the x- axis, are

x = - 4 , x = - 2 , x = - 1 , then the corresponding factors are

(x - (- 4)) , (x - (- 2)) , (x - (- 1)) , that is

(x + 4) , (x + 2) , (x + 1)

f(x) is then the product of these factors, that is

f(x) = (x + 2)(x + 1)(x + 4) ← in factored form