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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.
2. Calculate the expression [tex]\( -5x^2 \)[/tex].
[tex]\[
-5(3)^2 = -5 \times 9 = -45
\][/tex]
3. Calculate the expression [tex]\( -x \)[/tex].
[tex]\[
-3 = -3
\][/tex]
4. Add the constant term [tex]\( 20 \)[/tex].
[tex]\[
20 = 20
\][/tex]
5. Combine all the terms:
[tex]\[
-45 - 3 + 20
\][/tex]
6. First, add [tex]\(-45\)[/tex] and [tex]\(-3\)[/tex]:
[tex]\[
-45 - 3 = -48
\][/tex]
7. Then add [tex]\(20\)[/tex] to [tex]\(-48\)[/tex]:
[tex]\[
-48 + 20 = -28
\][/tex]
So, [tex]\( f(3) = -28 \)[/tex].
1. Substitute [tex]\( x = 3 \)[/tex] into the function.
2. Calculate the expression [tex]\( -5x^2 \)[/tex].
[tex]\[
-5(3)^2 = -5 \times 9 = -45
\][/tex]
3. Calculate the expression [tex]\( -x \)[/tex].
[tex]\[
-3 = -3
\][/tex]
4. Add the constant term [tex]\( 20 \)[/tex].
[tex]\[
20 = 20
\][/tex]
5. Combine all the terms:
[tex]\[
-45 - 3 + 20
\][/tex]
6. First, add [tex]\(-45\)[/tex] and [tex]\(-3\)[/tex]:
[tex]\[
-45 - 3 = -48
\][/tex]
7. Then add [tex]\(20\)[/tex] to [tex]\(-48\)[/tex]:
[tex]\[
-48 + 20 = -28
\][/tex]
So, [tex]\( f(3) = -28 \)[/tex].
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