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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]

and we need to calculate the value of [tex]$f(3)$[/tex].

Step 1. Substitute [tex]$x = 3$[/tex]:

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

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

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

Step 3. Multiply [tex]$9$[/tex] by [tex]$-5$[/tex]:

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

Step 4. Replace back into the function:

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

Step 5. Perform the additions:

Start by adding [tex]$-45$[/tex] and [tex]$-3$[/tex]:

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

Then add [tex]$20$[/tex] to [tex]$-48$[/tex]:

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

Thus, the value of the function at [tex]$x=3$[/tex] is

[tex]$$
f(3) = -28.
$$[/tex]

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