To find the value of the function [tex]\( f(x) = -2x^2 - 3x + 11 \)[/tex] at [tex]\( x = -3 \)[/tex], we'll substitute [tex]\( -3 \)[/tex] for [tex]\( x \)[/tex] in the function and simplify step-by-step.
1. Start with the given function:
[tex]\[
f(x) = -2x^2 - 3x + 11
\][/tex]
2. Substitute [tex]\( x = -3 \)[/tex] into the function:
[tex]\[
f(-3) = -2(-3)^2 - 3(-3) + 11
\][/tex]
3. Calculate [tex]\( (-3)^2 \)[/tex]:
[tex]\[
(-3)^2 = 9
\][/tex]
4. Substitute [tex]\( 9 \)[/tex] back into the function:
[tex]\[
f(-3) = -2(9) - 3(-3) + 11
\][/tex]
5. Multiply [tex]\( -2 \)[/tex] by [tex]\( 9 \)[/tex]:
[tex]\[
-2 \times 9 = -18
\][/tex]
6. Multiply [tex]\( -3 \)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[
-3 \times -3 = 9
\][/tex]
7. Substitute these values back into the function:
[tex]\[
f(-3) = -18 + 9 + 11
\][/tex]
8. Add [tex]\( -18 \)[/tex] and [tex]\( 9 \)[/tex]:
[tex]\[
-18 + 9 = -9
\][/tex]
9. Finally, add [tex]\( -9 \)[/tex] and [tex]\( 11 \)[/tex]:
[tex]\[
-9 + 11 = 2
\][/tex]
Therefore, the value of [tex]\( f(-3) \)[/tex] is [tex]\( 2 \)[/tex].
