Question

select the correct answer. which function represents a function with zeros at -3, -1, 0, and 6? a. $y=(x - 6)(x + 1)(x + 3)$ b. $y = x(x - 3)(x - 1)(x + 6)$ c. $y = x(x - 6)(x + 1)(x + 3)$ d. $y = (x - 3)(x - 1)(x + 6)$

Explanation:

Step1: Recall zero-product property

If $x=a$ is a zero, $(x-a)$ is a factor.

Step2: Convert zeros to factors

Zeros at $-3,-1,0,6$ give factors: $(x+3),(x+1),x,(x-6)$.

Step3: Combine factors into function

Multiply factors: $y = x(x - 6)(x + 1)(x + 3)$

Step4: Match to options

This matches option C.

Answer:

C. $y = x(x - 6)(x + 1)(x + 3)$