The graph of a quadratic function f(x) intersects the x-axis at -3 and 5.

What is a possible equation for f(x)?

What is a possible equation for f(x)?

Work backwards from the x-intercepts to arrive at the equation.

x = -3 and x = 5

x + 3 = 0 and x - 5 = 0 {added 3 to each side of first equation and added 5 to each side of second equation}

(x + 3)(x - 5) = 0 {multiplied the two binomials together and set equal to zero}

x² - 2x - 15 = 0 {muliplied the two binomials using FOIL method or distributive property}

x = -3 and x = 5

x + 3 = 0 and x - 5 = 0 {added 3 to each side of first equation and added 5 to each side of second equation}

(x + 3)(x - 5) = 0 {multiplied the two binomials together and set equal to zero}

x² - 2x - 15 = 0 {muliplied the two binomials using FOIL method or distributive property}

**f(x) = x² - 2x - 15**{replaced 0 with f(x) to write in function notation}

**- Algebra House**