Finding the Equation of a Polynomial Function In this section we will work backwards with the roots of polynomial equations or zeros of polynomial
functions. As we did with quadratics, so we will do with polynomials greater than second degree. Given
the roots of an equation, work backwards to find the polynomial equation or function from whence they
came. Recall the following example.
Find the equation of a parabola that has x intercepts of (−3,0 2,0 . ) and ( )
(−3,0 2,0 . ) and ( ) Given x intercepts of -3 and 2
x x =− = 3 2 If the x intercepts are -3 and 2, then the roots of the equation are -3 and 2. Set each

root equal to zero.

( x x + − 3 2 ) ( ) For the first root, add 3 to both sides of the equal sign.
For the second root, subtract 2 to both sides of the equal sign.

2
x x + − 6 Multiply the results together to find a quadratic expression.
2
yx x = +−6 Set the expression equal to y, or ( x) f , to write as the equation of a parabola.
The exercises in this section will result in polynomials greater than second degree. Be aware, you may not
be given all roots with which to work.

Consider the following example:
Find a polynomial function that has zeros of 0, 3 2 3 and i + . Although only three zeros are given here,− −+ . Multiplying