Final answer:
The function with zeros of -4 and 2 is g(x)=x^2-2x-8. It is derived from factors (x + 4) and (x - 2) that make the function zero.
Step-by-step explanation:
The function that has zeros of -4 and 2 is represented by the factors (x + 4) and (x - 2), which when multiplied together give a quadratic equation. A zero of a function is a value of x that makes the function equal to zero. So we are looking for a quadratic function of the form:
f(x) = a(x + 4)(x - 2)
Expanding this product, we have:
f(x) = a(x^2 - 2x + 4x - 8)
f(x) = a(x^2 + 2x - 8)
To match this form with the given options, we can set a = 1 (since the leading coefficient is not specified and can be assumed to be 1 for simplicity). Therefore, when a = 1, the function becomes:
f(x) = x^2 + 2x - 8
This function simplifies to the given option g(x)=x^2-2x-8, which has the required zeros of -4 and 2.