Answer :
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]\( f(x) = -5x^2 - x + 20 \)[/tex].
2. First, calculate [tex]\( -5x^2 \)[/tex] when [tex]\( x = 3 \)[/tex]:
[tex]\[
-5 \times 3^2 = -5 \times 9 = -45
\][/tex]
3. Next, calculate [tex]\(-x\)[/tex] when [tex]\( x = 3 \)[/tex]:
[tex]\[
-3
\][/tex]
4. Add these results along with the constant term [tex]\( 20 \)[/tex]:
[tex]\[
-45 - 3 + 20
\][/tex]
5. Combine these values step by step:
- First, add [tex]\(-45\)[/tex] and [tex]\(-3\)[/tex]:
[tex]\[
-45 - 3 = -48
\][/tex]
- Then, add [tex]\(-48\)[/tex] and [tex]\(20\)[/tex]:
[tex]\[
-48 + 20 = -28
\][/tex]
Therefore, [tex]\( f(3) = -28 \)[/tex].
So the correct answer is [tex]\(-28\)[/tex].
1. Substitute [tex]\( x = 3 \)[/tex] into the function [tex]\( f(x) = -5x^2 - x + 20 \)[/tex].
2. First, calculate [tex]\( -5x^2 \)[/tex] when [tex]\( x = 3 \)[/tex]:
[tex]\[
-5 \times 3^2 = -5 \times 9 = -45
\][/tex]
3. Next, calculate [tex]\(-x\)[/tex] when [tex]\( x = 3 \)[/tex]:
[tex]\[
-3
\][/tex]
4. Add these results along with the constant term [tex]\( 20 \)[/tex]:
[tex]\[
-45 - 3 + 20
\][/tex]
5. Combine these values step by step:
- First, add [tex]\(-45\)[/tex] and [tex]\(-3\)[/tex]:
[tex]\[
-45 - 3 = -48
\][/tex]
- Then, add [tex]\(-48\)[/tex] and [tex]\(20\)[/tex]:
[tex]\[
-48 + 20 = -28
\][/tex]
Therefore, [tex]\( f(3) = -28 \)[/tex].
So the correct answer is [tex]\(-28\)[/tex].
