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. 62
D. 64

Answer :

We need to evaluate the function
[tex]$$
f(x) = -5x^2 - x + 20
$$[/tex]
at [tex]$x = 3$[/tex]. Follow these steps:

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

2. Compute the square:
[tex]$$
3^2 = 9.
$$[/tex]

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

4. Compute the linear term:
[tex]$$
-3.
$$[/tex]

5. Now combine the terms:
[tex]$$
f(3) = -45 - 3 + 20.
$$[/tex]

6. Add the numbers step by step:
[tex]$$
-45 - 3 = -48,
$$[/tex]
and then
[tex]$$
-48 + 20 = -28.
$$[/tex]

Thus, the final answer is
[tex]$$
\boxed{-28}.
$$[/tex]