Sure, let's evaluate the function [tex]\( f(x) = -2x^2 - 3x + 5 \)[/tex] for the input value [tex]\( x = -3 \)[/tex].
1. Start by substituting [tex]\( x = -3 \)[/tex] into the function:
[tex]\[
f(-3) = -2(-3)^2 - 3(-3) + 5
\][/tex]
2. Calculate [tex]\( (-3)^2 \)[/tex]:
[tex]\[
(-3)^2 = 9
\][/tex]
3. Substitute this value back into the function:
[tex]\[
f(-3) = -2(9) - 3(-3) + 5
\][/tex]
4. Now multiply [tex]\(-2\)[/tex] by [tex]\(9\)[/tex]:
[tex]\[
-2 \times 9 = -18
\][/tex]
5. Next, calculate [tex]\(-3(-3)\)[/tex]:
[tex]\[
-3 \times -3 = 9
\][/tex]
6. Substitute these values back into the function:
[tex]\[
f(-3) = -18 + 9 + 5
\][/tex]
7. Now, combine the constants:
[tex]\[
-18 + 9 = -9
\][/tex]
[tex]\[
-9 + 5 = -4
\][/tex]
Therefore, [tex]\( f(-3) = -4 \)[/tex].
So, the correct answer is:
[tex]$ -4 $[/tex]
