Answer :
We start with the function
[tex]$$
f(x) = -5x^2 - x + 20.
$$[/tex]
To find [tex]$f(3)$[/tex], substitute [tex]$x = 3$[/tex] into the function:
[tex]$$
f(3) = -5(3)^2 - 3 + 20.
$$[/tex]
Step 1: Evaluate the squared term
Calculate the square of [tex]$3$[/tex]:
[tex]$$
3^2 = 9.
$$[/tex]
Step 2: Multiply by [tex]$-5$[/tex]
Multiply [tex]$9$[/tex] by [tex]$-5$[/tex]:
[tex]$$
-5 \times 9 = -45.
$$[/tex]
Step 3: Combine the terms
Now, substitute back into the equation:
[tex]$$
f(3) = -45 - 3 + 20.
$$[/tex]
First, combine [tex]$-45$[/tex] and [tex]$-3$[/tex]:
[tex]$$
-45 - 3 = -48.
$$[/tex]
Then add [tex]$20$[/tex]:
[tex]$$
-48 + 20 = -28.
$$[/tex]
Thus, the value of [tex]$f(3)$[/tex] is
[tex]$$
\boxed{-28}.
$$[/tex]
[tex]$$
f(x) = -5x^2 - x + 20.
$$[/tex]
To find [tex]$f(3)$[/tex], substitute [tex]$x = 3$[/tex] into the function:
[tex]$$
f(3) = -5(3)^2 - 3 + 20.
$$[/tex]
Step 1: Evaluate the squared term
Calculate the square of [tex]$3$[/tex]:
[tex]$$
3^2 = 9.
$$[/tex]
Step 2: Multiply by [tex]$-5$[/tex]
Multiply [tex]$9$[/tex] by [tex]$-5$[/tex]:
[tex]$$
-5 \times 9 = -45.
$$[/tex]
Step 3: Combine the terms
Now, substitute back into the equation:
[tex]$$
f(3) = -45 - 3 + 20.
$$[/tex]
First, combine [tex]$-45$[/tex] and [tex]$-3$[/tex]:
[tex]$$
-45 - 3 = -48.
$$[/tex]
Then add [tex]$20$[/tex]:
[tex]$$
-48 + 20 = -28.
$$[/tex]
Thus, the value of [tex]$f(3)$[/tex] is
[tex]$$
\boxed{-28}.
$$[/tex]
