Answer :
To find [tex]\( f(3) \)[/tex] for the function [tex]\( f(x) = -5x^2 - x + 20 \)[/tex], we need to evaluate the function at [tex]\( x = 3 \)[/tex].
Here are the steps:
1. Substitute [tex]\( x = 3 \)[/tex] into the function [tex]\( f(x) = -5x^2 - x + 20 \)[/tex].
2. Calculate each part of the expression:
- First, calculate [tex]\( -5 \times 3^2 \)[/tex]:
[tex]\[
-5 \times 3^2 = -5 \times 9 = -45
\][/tex]
- Next, calculate [tex]\( -x \)[/tex] when [tex]\( x = 3 \)[/tex]:
[tex]\[
-3 = -3
\][/tex]
- Finally, add 20:
[tex]\[
20 = 20
\][/tex]
3. Combine all the parts together:
- Add [tex]\(-45\)[/tex], [tex]\(-3\)[/tex], and [tex]\(20\)[/tex]:
[tex]\[
-45 - 3 + 20 = -28
\][/tex]
Therefore, the value of [tex]\( f(3) \)[/tex] is [tex]\(-28\)[/tex].
So, the correct option is: [tex]\(-28\)[/tex].
Here are the steps:
1. Substitute [tex]\( x = 3 \)[/tex] into the function [tex]\( f(x) = -5x^2 - x + 20 \)[/tex].
2. Calculate each part of the expression:
- First, calculate [tex]\( -5 \times 3^2 \)[/tex]:
[tex]\[
-5 \times 3^2 = -5 \times 9 = -45
\][/tex]
- Next, calculate [tex]\( -x \)[/tex] when [tex]\( x = 3 \)[/tex]:
[tex]\[
-3 = -3
\][/tex]
- Finally, add 20:
[tex]\[
20 = 20
\][/tex]
3. Combine all the parts together:
- Add [tex]\(-45\)[/tex], [tex]\(-3\)[/tex], and [tex]\(20\)[/tex]:
[tex]\[
-45 - 3 + 20 = -28
\][/tex]
Therefore, the value of [tex]\( f(3) \)[/tex] is [tex]\(-28\)[/tex].
So, the correct option is: [tex]\(-28\)[/tex].
