# If f(x)=4x^2-24x+36, how do you find the value f(x)=4?

Jul 27, 2015

You know that your function looks like this

$f \left(x\right) = 4 {x}^{2} - 24 x + 36$

If $f \left(x\right) = 4$, then you can say that

$f \left(x\right) = 4 {x}^{2} - 24 x + 36 = 4$

Get this equation in quadratic form by adding $- 4$ to both sides of the equation

$4 {x}^{2} - 24 x + 36 - 4 = \textcolor{red}{\cancel{\textcolor{b l a c k}{4}}} - \textcolor{red}{\cancel{\textcolor{b l a c k}{4}}}$

$4 {x}^{2} - 24 x + 32 = 0$

This is equivalent ot

$4 \left({x}^{2} - 6 x + 8\right) = 0$

You can use the quadratic formula to get the two solutions for this equation

${x}_{1 , 2} = \frac{- \left(- 6\right) \pm \sqrt{{\left(- 6\right)}^{2} - 4 \cdot 1 \cdot 8}}{2}$

${x}_{1 , 2} = \frac{6 \pm \sqrt{36 - 32}}{2}$

${x}_{1 , 2} = \frac{6 \pm 2}{2} = \left\{\begin{matrix}{x}_{1} = 4 \\ {x}_{2} = 2\end{matrix}\right.$

This means that you have two values of $x$ for which $f \left(x\right)$ is equal to $4$.

$f \left(2\right) = 4$ and $f \left(4\right) = 4$