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