A quadratic polynomial $p(x)$ is such that $p(x)$ never takes any negative values. Also, $p(0)=8$ and $p(8)=0$. What would $p(-4)$ be?
I tried doing it by taking the minimum value as zero that is the vertex of the polynomial at $8$. How do we go about after finding out values of $a$ and $b$ in the standard form of the equation $ax^2 + bx + c$ ? Could this be done in a shorter way graphically?