Question

select the correct answer.
the zeros of a quadratic function are 6 and -4. which of these choices could be the function?
a. $f(x) = (x + 6)(x + 4)$
b. $f(x) = (x + 6)(x - 4)$
c. $f(x) = (x - 6)(x - 4)$
d. $f(x) = (x - 6)(x + 4)$

Explanation:

Step1: Recall zero factor principle

If $r$ is a zero of $f(x)$, then $(x-r)$ is a factor.

Step2: Identify factors from zeros

For zero $6$: factor is $(x-6)$; for zero $-4$: factor is $(x-(-4))=(x+4)$.

Step3: Form the quadratic function

Multiply the factors: $f(x)=(x-6)(x+4)$.

Answer:

D. $f(x) = (x - 6)(x + 4)$