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Answer :
To find [tex]\( f(3) \)[/tex] for the given function [tex]\( f(x) = -5x^2 - x + 20 \)[/tex], follow these steps:
1. Start with the function:
[tex]\[
f(x) = -5x^2 - x + 20
\][/tex]
2. Substitute [tex]\( x = 3 \)[/tex] into the function:
[tex]\[
f(3) = -5(3)^2 - 3 + 20
\][/tex]
3. Calculate [tex]\( (3)^2 \)[/tex]:
[tex]\[
(3)^2 = 9
\][/tex]
4. Multiply [tex]\( 9 \)[/tex] by [tex]\(-5\)[/tex]:
[tex]\[
-5 \times 9 = -45
\][/tex]
5. Add the next term, which is [tex]\(-3\)[/tex]:
[tex]\[
-45 - 3 = -48
\][/tex]
6. Finally, add 20 to [tex]\(-48\)[/tex]:
[tex]\[
-48 + 20 = -28
\][/tex]
So, [tex]\( f(3) = -28 \)[/tex].
Therefore, the correct answer is:
[tex]\[
-28
\][/tex]
1. Start with the function:
[tex]\[
f(x) = -5x^2 - x + 20
\][/tex]
2. Substitute [tex]\( x = 3 \)[/tex] into the function:
[tex]\[
f(3) = -5(3)^2 - 3 + 20
\][/tex]
3. Calculate [tex]\( (3)^2 \)[/tex]:
[tex]\[
(3)^2 = 9
\][/tex]
4. Multiply [tex]\( 9 \)[/tex] by [tex]\(-5\)[/tex]:
[tex]\[
-5 \times 9 = -45
\][/tex]
5. Add the next term, which is [tex]\(-3\)[/tex]:
[tex]\[
-45 - 3 = -48
\][/tex]
6. Finally, add 20 to [tex]\(-48\)[/tex]:
[tex]\[
-48 + 20 = -28
\][/tex]
So, [tex]\( f(3) = -28 \)[/tex].
Therefore, the correct answer is:
[tex]\[
-28
\][/tex]
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