College

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

A. -28
B. -13
C. 62
D. 64

Answer :

To find [tex]\( f(3) \)[/tex] for the function [tex]\( f(x) = -5x^2 - x + 20 \)[/tex], we need to evaluate the function at [tex]\( x = 3 \)[/tex].

Here are the steps:

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

2. Calculate each part of the expression:
- First, calculate [tex]\( -5 \times 3^2 \)[/tex]:
[tex]\[
-5 \times 3^2 = -5 \times 9 = -45
\][/tex]

- Next, calculate [tex]\( -x \)[/tex] when [tex]\( x = 3 \)[/tex]:
[tex]\[
-3 = -3
\][/tex]

- Finally, add 20:
[tex]\[
20 = 20
\][/tex]

3. Combine all the parts together:
- Add [tex]\(-45\)[/tex], [tex]\(-3\)[/tex], and [tex]\(20\)[/tex]:
[tex]\[
-45 - 3 + 20 = -28
\][/tex]

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

So, the correct option is: [tex]\(-28\)[/tex].