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Answer :
Sure, let's find [tex]\( f(3) \)[/tex] for the function [tex]\( f(x) = -5x^2 - x + 20 \)[/tex].
1. Substitute [tex]\( x = 3 \)[/tex] into the function:
[tex]\[
f(3) = -5(3)^2 - 3 + 20
\][/tex]
2. Calculate the square:
[tex]\[
3^2 = 9
\][/tex]
3. Multiply by -5:
[tex]\[
-5 \cdot 9 = -45
\][/tex]
4. Substitute back into the expression:
[tex]\[
f(3) = -45 - 3 + 20
\][/tex]
5. Combine the terms:
[tex]\[
-45 - 3 = -48
\][/tex]
and then,
[tex]\[
-48 + 20 = -28
\][/tex]
So, [tex]\( f(3) = -28 \)[/tex].
Therefore, the correct answer is [tex]\( -28 \)[/tex].
1. Substitute [tex]\( x = 3 \)[/tex] into the function:
[tex]\[
f(3) = -5(3)^2 - 3 + 20
\][/tex]
2. Calculate the square:
[tex]\[
3^2 = 9
\][/tex]
3. Multiply by -5:
[tex]\[
-5 \cdot 9 = -45
\][/tex]
4. Substitute back into the expression:
[tex]\[
f(3) = -45 - 3 + 20
\][/tex]
5. Combine the terms:
[tex]\[
-45 - 3 = -48
\][/tex]
and then,
[tex]\[
-48 + 20 = -28
\][/tex]
So, [tex]\( f(3) = -28 \)[/tex].
Therefore, the correct answer is [tex]\( -28 \)[/tex].
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