What is the maximum value of $4(x + 7)(2 - x)$, over all real numbers $x$?
First, convert into vertex form by first foiling (x+7) and (2-x), which turns the equation into \(4(-x^2-7x+2x+14)\) = \(4(-x^2-5x+14) = -4x^2-20x+56\). Then, use -b/2a to find the x-coordinate of the vertex \(20 \over 2*-4\)=-5/2. Then, just plug -5/2 into the equation to get the y-coordinate. The vertex in this case is the maximum of because the leading coefficient is negative for a quadratic equation.