College

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], you simply need to evaluate the function at [tex]\( x = 3 \)[/tex]. Here is how you can do it step-by-step:

1. Plug in the value of [tex]\( x = 3 \)[/tex] into the function:

[tex]\[
f(3) = -5(3)^2 - (3) + 20
\][/tex]

2. Calculate [tex]\( (3)^2 \)[/tex]:

[tex]\[
3^2 = 9
\][/tex]

3. Multiply -5 by 9:

[tex]\[
-5 \times 9 = -45
\][/tex]

4. Substitute back into the function:

[tex]\[
f(3) = -45 - 3 + 20
\][/tex]

5. Simplify the expression step-by-step:

- First, add the [tex]\(-45\)[/tex] and [tex]\(-3\)[/tex]:

[tex]\[
-45 - 3 = -48
\][/tex]

- Then, add [tex]\(20\)[/tex]:

[tex]\[
-48 + 20 = -28
\][/tex]

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