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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], follow these steps:

1. Substitute [tex]\( x = 3 \)[/tex] into the function:
Plug 3 into the function in place of [tex]\( x \)[/tex]:
[tex]\[
f(3) = -5(3)^2 - (3) + 20
\][/tex]

2. Calculate [tex]\( 3^2 \)[/tex]:
First, calculate [tex]\( 3^2 \)[/tex]:
[tex]\[
3^2 = 9
\][/tex]

3. Multiply by [tex]\(-5\)[/tex]:
Multiply 9 by [tex]\(-5\)[/tex]:
[tex]\[
-5 \times 9 = -45
\][/tex]

4. Complete the rest of the function:
Substitute the values back:
[tex]\[
f(3) = -45 - 3 + 20
\][/tex]

5. Simplify step-by-step:
- First, compute [tex]\(-45 - 3\)[/tex]:
[tex]\[
-45 - 3 = -48
\][/tex]
- Then add 20:
[tex]\[
-48 + 20 = -28
\][/tex]

Thus, [tex]\( f(3) = -28 \)[/tex]. Therefore, the value of [tex]\( f(3) \)[/tex] is [tex]\(-28\)[/tex].

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