To find [tex]\( f(3) \)[/tex] for the function [tex]\( f(x) = -5x^2 - x + 20 \)[/tex], follow these steps:
1. Substitute [tex]\( x = 3 \)[/tex] into the function:
[tex]\[
f(3) = -5(3)^2 - 3 + 20
\][/tex]
2. Calculate the square of 3:
[tex]\[
3^2 = 9
\][/tex]
3. Multiply the squared value by -5:
[tex]\[
-5 \cdot 9 = -45
\][/tex]
4. Add the linear term (-3):
[tex]\[
-45 - 3 = -48
\][/tex]
5. Finally, add the constant term (20):
[tex]\[
-48 + 20 = -28
\][/tex]
Thus, the value of [tex]\( f(3) \)[/tex] is [tex]\(-28\)[/tex].
The correct answer is [tex]\(\boxed{-28}\)[/tex].
