To find the value of [tex]\( f(5) \)[/tex] when [tex]\( f(x) = -2x^2 + 2x - 3 \)[/tex], follow these steps:
1. Substitute [tex]\( x = 5 \)[/tex] into the function [tex]\( f(x) \)[/tex]:
[tex]\[
f(5) = -2(5)^2 + 2(5) - 3
\][/tex]
2. Calculate the value inside the parentheses. First, determine [tex]\( 5^2 \)[/tex]:
[tex]\[
5^2 = 25
\][/tex]
3. Multiply [tex]\( -2 \)[/tex] by [tex]\( 25 \)[/tex]:
[tex]\[
-2 \times 25 = -50
\][/tex]
4. Next, multiply [tex]\( 2 \)[/tex] by [tex]\( 5 \)[/tex]:
[tex]\[
2 \times 5 = 10
\][/tex]
5. Combine the results from steps 2, 3, and 4:
[tex]\[
f(5) = -50 + 10 - 3
\][/tex]
6. Perform the addition and subtraction in order:
[tex]\[
-50 + 10 = -40
\][/tex]
[tex]\[
-40 - 3 = -43
\][/tex]
So, the value of [tex]\( f(5) \)[/tex] is:
[tex]\[
f(5) = -43
\][/tex]
Thus, the correct answer is:
[tex]\[
-43
\][/tex]
