Final answer:
The correct factored form of the quadratic function f(x) = -16x^2 + 60x + 16 is -16(x - 4)(x + 4), as it satisfies the condition of factoring a quadratic equation.
Step-by-step explanation:
To factor the quadratic function f(x) = -16x^2 + 60x + 16, we must find two binomials that multiply to give the original quadratic equation. We look for two numbers that multiply to give the product of the coefficient of x^2 (which is -16) and the constant term (which is +16), and add to give the coefficient of x (which is +60).
Upon inspection, we see that the numbers +64 and -4 satisfy these conditions because (64)(-4) = -256 and 64 - 4 = 60. So we can rewrite the quadratic equation as:
f(x) = -16(x - 4)(x + 4)
It's the distributive property in reverse, also called factoring. To check our work, we can distribute the binomials back out and confirm they give us our original equation.