Question 254·Easy·Math

The given $p(a)=0$ says the output must be $0$, so replace $p(a)$ with its rule: $a^2+4a-12=0$. An input that makes this equation true is a zero of $p$.

Type $p(x)=x^2+4x-12$ in Desmos; $x$ names the input on its graph. Click both $x$-intercepts. Desmos labels them $(-6,0)$ and $(2,0)$. At an intercept, the first coordinate is the input that makes the output $0$. Only $2$ is listed, so $a=2$. Choice C.

Factoring rewrites a sum as a product. The numbers $6$ and $-2$ multiply to $-12$ and add to $4$, so they give the needed factors:

Since $p(a)=0$, the product equals $0$. The zero-product property says at least one factor must be $0$, so:

Subtract $6$ from $a+6=0$: $a=-6$. This zero isn’t among the choices.

Add $2$ to $a-2=0$: $a=2$. This zero is listed, so it’s the requested value of $a$. Choice C.