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Given the function [tex]$f(x) = -5x^2 - x + 20$[/tex], find [tex]$f(3)$[/tex].

A. [tex]-28[/tex]
B. [tex]-13[/tex]
C. [tex]62[/tex]
D. [tex]64[/tex]

Answer :

To find [tex]\( f(3) \)[/tex] for the function [tex]\( f(x) = -5x^2 - x + 20 \)[/tex], we need to substitute [tex]\( x = 3 \)[/tex] into the function and perform the calculations step by step.

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 the square of 3:
[tex]\[
3^2 = 9
\][/tex]

4. Multiply this result by -5:
[tex]\[
-5 \times 9 = -45
\][/tex]

5. Now substitute these values back into the function expression:
[tex]\[
f(3) = -45 - 3 + 20
\][/tex]

6. Calculate the expression from left to right:
[tex]\[
-45 - 3 = -48
\][/tex]

7. Finally, add 20 to the result:
[tex]\[
-48 + 20 = -28
\][/tex]

Therefore, [tex]\( f(3) = -28 \)[/tex].

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