To find [tex]\( f(-6) \)[/tex] given the function [tex]\( f(x) = 2x^2 - x \)[/tex], we need to substitute [tex]\( x \)[/tex] with [tex]\(-6\)[/tex] and evaluate the expression step-by-step:
1. Start with the function: [tex]\( f(x) = 2x^2 - x \)[/tex].
2. Substitute [tex]\( x = -6 \)[/tex] into the function:
[tex]\[
f(-6) = 2(-6)^2 - (-6)
\][/tex]
3. Calculate [tex]\((-6)^2\)[/tex]:
[tex]\[
(-6)^2 = 36
\][/tex]
4. Multiply this result by 2 (since [tex]\( 2 \cdot 36 \)[/tex]):
[tex]\[
2 \cdot 36 = 72
\][/tex]
5. The function now looks like:
[tex]\[
f(-6) = 72 + 6
\][/tex]
6. Add 6 to 72:
[tex]\[
72 + 6 = 78
\][/tex]
Therefore, the value of [tex]\( f(-6) \)[/tex] is [tex]\( 78 \)[/tex].
Among the answer choices, the correct one is:
[tex]\[
\boxed{78}
\][/tex]
