Write a quadratic function f whose zeros are 2 and 9.

A quadratic function, when factored, is written as two binomials e. g. (x+2) (x-1), right? When we set each binomial equal to zero and solve, we get the x-intercepts of the graph ... the zeros of the quadratic.

For this system, x=2 and x=9 are the zeros.

Therefore (x-2) and (x-9) are the binomials which solve to those zeros.

Multiply the binomials together to get the quadratic:

(x-2) (x-9) = x² - 11x + 18

f (x) = x² - 11x + 18