# Thread: How to find a Quadratic Function when given the zeros

1. ## How to find a Quadratic Function when given the zeros

Give a quadratic function with zeros at x=3 and x= -4.
I know how to solve a quadratic equation, but have no idea where to begin when given the answer first.

2. ## Re: How to find a Quadratic Function when given the zeros

Originally Posted by Ray1357
Give a quadratic function with zeros at x=3 and x= -4.
I know how to solve a quadratic equation, but have no idea where to begin when given the answer first.
If x = a is a root of the polynomial, then (x - a) is a factor.
So we have factors (x - 3) and (x - -4) = (x + 4)

f(x) = c(x - 3)(x + 4), where c is not 0

If you were going to solve a quadratic equation by factoring (such as x^2 - x - 6 = 0), you would use the "zero product property" to set each factor equal to zero.

(x - 3)(x + 2) = 0 -->
x - 3 = 0 or x + 2 = 0
<-->
x = 3 or x = -2.

When you are given the roots, you reverse the process. Notice that the solutions to
(x - 3)(x + 2) = 0 don't change if you multiply this equation by a nonzero constant, so this would give us
c(x - 3)(x + 2) = 0 as in the given problem.

3. ## Re: How to find a Quadratic Function when given the zeros

That makes complete sense, thank you!

4. ## Re: How to find a Quadratic Function when given the zeros

Originally Posted by Ray1357
That makes complete sense, thank you!
No problemo!
Welcome to the forums.