To find [tex]\( F(-4) \)[/tex], we will substitute [tex]\( x = -4 \)[/tex] into the polynomial function [tex]\( F(x) = 2x^2 - x + 9 \)[/tex] and then simplify.
1. Substitute [tex]\( x = -4 \)[/tex] into the function [tex]\( F(x) \)[/tex]:
[tex]\[
F(-4) = 2(-4)^2 - (-4) + 9
\][/tex]
2. Calculate [tex]\((-4)^2\)[/tex]:
[tex]\[
(-4)^2 = 16
\][/tex]
3. Multiply [tex]\(2\)[/tex] by [tex]\(16\)[/tex]:
[tex]\[
2 \times 16 = 32
\][/tex]
4. Simplify [tex]\(- (-4)\)[/tex]:
[tex]\[
-(-4) = 4
\][/tex]
5. Add the terms together:
[tex]\[
F(-4) = 32 + 4 + 9
\][/tex]
6. Finally, perform the addition:
[tex]\[
32 + 4 = 36
\][/tex]
[tex]\[
36 + 9 = 45
\][/tex]
Thus, the value of [tex]\( F(-4) \)[/tex] is 45. Therefore, the correct answer is:
B. 45
