To evaluate [tex]\( f(-6) \)[/tex] for the function [tex]\( f(x) = 2x^2 + 5x - \frac{x}{3} \)[/tex], follow these steps:
1. Substitute [tex]\( x = -6 \)[/tex] into the function:
[tex]\[
f(-6) = 2(-6)^2 + 5(-6) - \frac{-6}{3}
\][/tex]
2. Calculate each term individually:
- First term: [tex]\( 2(-6)^2 \)[/tex]
[tex]\[
(-6)^2 = 36
\][/tex]
[tex]\[
2 \times 36 = 72
\][/tex]
- Second term: [tex]\( 5(-6) \)[/tex]
[tex]\[
5 \times (-6) = -30
\][/tex]
- Third term: [tex]\( -\frac{-6}{3} \)[/tex]
[tex]\[
\frac{-6}{3} = -2
\][/tex]
[tex]\[
-(-2) = 2
\][/tex]
3. Combine the results:
[tex]\[
f(-6) = 72 - 30 + 2
\][/tex]
4. Simplify the expression:
[tex]\[
f(-6) = 72 - 30 + 2 = 44
\][/tex]
Therefore, the value of [tex]\( f(-6) \)[/tex] is [tex]\( 44.0 \)[/tex].
