# For f(m)=3m^2-5, how do you find f(4),f(-3),f(6)?

Jul 8, 2015

$f \left(4\right) = 43$
$f \left(- 3\right) = 22$
$f \left(6\right) = 102$

#### Explanation:

Given $f \left(\textcolor{red}{m}\right) = 3 {\textcolor{red}{m}}^{2} - 5$

To evaluate $f \left(\textcolor{red}{} 4\right)$ rewrite the given equation replacing each $\textcolor{red}{m}$ with $\textcolor{red}{4}$ and perform the arithmetic.
$\textcolor{w h i t e}{\text{XXXX}}$$f \left(\textcolor{red}{4}\right) = 3 {\left(\textcolor{red}{4}\right)}^{2} - 5$
$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$$= 3 \left(16\right) - 5$
$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$$= 43$

Similarly for $f \left(\textcolor{red}{- 3}\right)$
$\textcolor{w h i t e}{\text{XXXX}}$$f \left(\textcolor{red}{- 3}\right) = 3 {\left(\textcolor{red}{- 3}\right)}^{2} - 5$
$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$$= 3 \left(9\right) - 5$
$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$$= 22$

and for $f \left(6\right)$
$\textcolor{w h i t e}{\text{XXXX}}$$f \left(\textcolor{red}{6}\right) = 3 {\left(\textcolor{red}{6}\right)}^{2} - 5$
$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$$= 3 \left(36\right) - 6$
$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$$= 102$