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]
[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]
