given the function $f(x)=-x^{2}-\frac{1}{6}x$, find the value of $f(2)$ in simplest form.

Explanation:

Step1: Substitute x = 2

Substitute $x = 2$ into $f(x)=-x^{2}-\frac{1}{6}x$. $f(2)=-(2)^{2}-\frac{1}{6}\times2$

Step2: Calculate powers and multiplications

First, calculate $(2)^{2}=4$ and $\frac{1}{6}\times2=\frac{1}{3}$. $f(2)=- 4-\frac{1}{3}$

Step3: Find a common - denominator and subtract

The common denominator of 1 and 3 is 3. So, $-4=-\frac{12}{3}$. $f(2)=-\frac{12}{3}-\frac{1}{3}=-\frac{12 + 1}{3}=-\frac{13}{3}$

Answer:

$-\frac{13}{3}$