# Given f(x)= x^2- 3x, how do you write the expression for f(a+ 2)?

Jan 6, 2017

$f \left(\textcolor{red}{a + 2}\right) = {a}^{2} + a - 2$

or

$f \left(\textcolor{red}{a + 2}\right) = \left(a + 2\right) \left(a - 1\right)$

#### Explanation:

We will need to substitute $\textcolor{red}{a + 2}$ for each occurrence of $\textcolor{b l u e}{x}$ in the original function.

$f \left(\textcolor{b l u e}{x}\right) = {\textcolor{b l u e}{x}}^{2} - 3 \textcolor{b l u e}{x}$

Becomes:

$f \left(\textcolor{red}{a + 2}\right) = {\left(\textcolor{red}{a + 2}\right)}^{2} - 3 \left(\textcolor{red}{a + 2}\right)$

$f \left(\textcolor{red}{a + 2}\right) = \left(\left(\textcolor{red}{a + 2}\right) \left(\textcolor{red}{a + 2}\right)\right) - 3 a - 6$

$f \left(\textcolor{red}{a + 2}\right) = \left({a}^{2} + 2 a + 2 a + 4\right) - 3 a - 6$

$f \left(\textcolor{red}{a + 2}\right) = {a}^{2} + 2 a + 2 a + 4 - 3 a - 6$

$f \left(\textcolor{red}{a + 2}\right) = {a}^{2} + 2 a + 2 a - 3 a + 4 - 6$

$f \left(\textcolor{red}{a + 2}\right) = {a}^{2} + a - 2$

or

$f \left(\textcolor{red}{a + 2}\right) = \left(a + 2\right) \left(a - 1\right)$