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 are given the function

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

To find [tex]$f(3)$[/tex], we substitute [tex]$x = 3$[/tex] into the equation:

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

Step 1: Calculate [tex]$3^2$[/tex]:

[tex]$$
3^2 = 9.
$$[/tex]

Step 2: Multiply by [tex]$-5$[/tex]:

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

Step 3: Substitute back into the function:

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

Step 4: Combine the terms:

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

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

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

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