# Give an example of a quadratic function that has zeroes at $x=2$ and $x=4$, and that takes the value $6$ when $x=3$.

I came across this problem while I was doing some math:

Give an example of a quadratic function that has zeroes at $x=2$ and $x=4$, and that takes the value $6$ when $x=3$.

First, I tried doing $(x-2)(x-4)$, but that doesn't have a value of $6$ when $x=3$.

How should I proceed?

Thank you!

• A quadratic function has the form $ax^2+bx+c$. Plug in what you got to see if you have enough to determine the values of $a$, $b$ and $c$. – mucciolo Nov 29 '17 at 2:44

Hint: Take $f(x)=a(x-2)(x-4)$ and set $f(3)=6$. Solve for $a$.