To evaluate [tex]\( f(-6) \)[/tex] for the given function [tex]\( f(x) = 2x^2 + 5x - \frac{x}{3} \)[/tex], we 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. Simplify each term individually:
- Calculate [tex]\( (-6)^2 \)[/tex]:
[tex]\[ (-6)^2 = 36 \][/tex]
- Multiply [tex]\( 2 \)[/tex] by the result of [tex]\( 36 \)[/tex]:
[tex]\[ 2 \cdot 36 = 72 \][/tex]
- Multiply [tex]\( 5 \)[/tex] by [tex]\( -6 \)[/tex]:
[tex]\[ 5 \cdot (-6) = -30 \][/tex]
- Divide [tex]\( -6 \)[/tex] by [tex]\( 3 \)[/tex]:
[tex]\[ -\frac{-6}{3} = 2 \][/tex]
3. Add the results of these terms together:
[tex]\[ 72 + (-30) + 2 \][/tex]
4. Simplify the expression by performing the arithmetic operations:
- First, add [tex]\( 72 \)[/tex] and [tex]\( -30 \)[/tex]:
[tex]\[ 72 - 30 = 42 \][/tex]
- Then, add [tex]\( 42 \)[/tex] and [tex]\( 2 \)[/tex]:
[tex]\[ 42 + 2 = 44 \][/tex]
So, the value of [tex]\( f(-6) \)[/tex] when simplified is:
[tex]\[ f(-6) = 44 \][/tex]
