Quadratic equation

Question

What is the quadratic equation of a graph with x intercepts of 2 and 4, and a vertex of 3,-5

Answer 1

Since 2 and 4 are roots, the equation must be a multiple of x² - 6x + 8 and 5 will serve the purpose:

5x² - 30x + 40. At x = 3, the quadratic has value -5. The easiest way to compute the multiplier is to substitute A(9 - 18 + 8) = -5 => A = 5.