Quadratics with Defined Roots in Standard Form

How does changing the values of a, b, and c affect the graph?  How can we ensure that the graph is symmetrical across x=4?

Originally the problem was going to call for two equations but then I realized that it could be as simply as multiplying the a, b, and c values by -1.  There are infinite answers, and here are four of them: x^2 + -8x + 15, -x^2 + 8x + -15, 10x^2 + -80x + 150, 2x^2 + -16x + 30.