To find the value of [tex]\( f(-3) \)[/tex] for the function [tex]\( f(a) = -2a^2 - 5a + 4 \)[/tex], we will follow these steps:
1. Substitute [tex]\( a = -3 \)[/tex] into the function:
[tex]\[
f(-3) = -2(-3)^2 - 5(-3) + 4
\][/tex]
2. Calculate the value of each term:
- First, compute [tex]\( (-3)^2 \)[/tex]:
[tex]\[
(-3)^2 = 9
\][/tex]
- Next, multiply by [tex]\(-2\)[/tex]:
[tex]\[
-2 \times 9 = -18
\][/tex]
- Then, compute [tex]\( -5 \times (-3) \)[/tex]:
[tex]\[
-5 \times (-3) = 15
\][/tex]
- The constant term remains the same:
[tex]\[
4
\][/tex]
3. Combine all the terms:
[tex]\[
f(-3) = -18 + 15 + 4
\][/tex]
4. Simplify the expression:
[tex]\[
-18 + 15 = -3
\][/tex]
Then,
[tex]\[
-3 + 4 = 1
\][/tex]
Therefore, [tex]\( f(-3) = 1 \)[/tex].
Hence, the correct answer is [tex]\( 1 \)[/tex].
