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 :

We are given the function

[tex]$$
f(x) = -5x^2 - x + 20.
$$[/tex]

To find [tex]$f(3)$[/tex], we follow these steps:

1. Substitute [tex]$x=3$[/tex] into the function:

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

2. Calculate 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]$$
-3 \quad \text{(since it's } -x \text{ and } x=3\text{)}.
$$[/tex]

5. Add all the terms together:

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

6. Simplify the expression:

[tex]$$
-45 - 3 = -48,
$$[/tex]

and then

[tex]$$
-48 + 20 = -28.
$$[/tex]

Thus, the value of [tex]$f(3)$[/tex] is

[tex]$$
\boxed{-28}.
$$[/tex]