A quadratic function has roots at x=4 and x=-3. Which equation could represent this function?

If the roots are $4$ and $-3$, the factors are $(x-4)$ and $(x+3)$. Multiply: $(x-4)(x+3)=x^2+3x-4x-12=x^2-x-12$, choice A. Check the roots: the sum $4+(-3)=1$ equals $-b$, and the product $-12$ equals $c$. Choice B ($x^2+x-12$) has roots $3$ and $-4$, with the middle sign reversed. Choice C ($x^2-7x+12$) has roots $3$ and $4$. Choice D ($x^2-x+12$) has the right middle term but a positive constant, which gives complex roots since the discriminant is $1-48<0$.