Find the quadratic function with the given x-intercepts

3/11/2017

The graph of a quadratic function intersects the x-axis at -3 and 5.
What is a possible equation for f(x) ?

Work backwards from the solutions to the equation.

x = -3 and x = 5
x + 3 = 0 and x - 5 = 0 {added 3 and subtracted 5 in the two equations}
(x + 3)(x - 5) = 0 {multiplied the two binomials and set equal to zero}
x² - 2x - 15 = 0 {used distributive property / FOIL method}
f(x) = x² - 2x - 15 {replaced 0 with f(x)}