Answer :
To find [tex]\( f(3) \)[/tex] for the function [tex]\( f(x) = -5x^2 - x + 20 \)[/tex], follow these steps:
1. Substitute [tex]\( x = 3 \)[/tex] into the function:
Start with the expression for the function:
[tex]\[
f(x) = -5x^2 - x + 20
\][/tex]
Replace [tex]\( x \)[/tex] with 3:
[tex]\[
f(3) = -5(3)^2 - (3) + 20
\][/tex]
2. Calculate the square:
Compute [tex]\( 3^2 \)[/tex]:
[tex]\[
3^2 = 9
\][/tex]
Substitute back into the equation:
[tex]\[
f(3) = -5(9) - 3 + 20
\][/tex]
3. Multiply and simplify:
Multiply [tex]\(-5\)[/tex] by 9:
[tex]\[
-5 \times 9 = -45
\][/tex]
Substitute the result back:
[tex]\[
f(3) = -45 - 3 + 20
\][/tex]
4. Combine the terms:
First, combine [tex]\(-45\)[/tex] and [tex]\(-3\)[/tex]:
[tex]\[
-45 - 3 = -48
\][/tex]
Then add 20:
[tex]\[
-48 + 20 = -28
\][/tex]
So, the final result is:
[tex]\[
f(3) = -28
\][/tex]
The correct answer is [tex]\(-28\)[/tex].
1. Substitute [tex]\( x = 3 \)[/tex] into the function:
Start with the expression for the function:
[tex]\[
f(x) = -5x^2 - x + 20
\][/tex]
Replace [tex]\( x \)[/tex] with 3:
[tex]\[
f(3) = -5(3)^2 - (3) + 20
\][/tex]
2. Calculate the square:
Compute [tex]\( 3^2 \)[/tex]:
[tex]\[
3^2 = 9
\][/tex]
Substitute back into the equation:
[tex]\[
f(3) = -5(9) - 3 + 20
\][/tex]
3. Multiply and simplify:
Multiply [tex]\(-5\)[/tex] by 9:
[tex]\[
-5 \times 9 = -45
\][/tex]
Substitute the result back:
[tex]\[
f(3) = -45 - 3 + 20
\][/tex]
4. Combine the terms:
First, combine [tex]\(-45\)[/tex] and [tex]\(-3\)[/tex]:
[tex]\[
-45 - 3 = -48
\][/tex]
Then add 20:
[tex]\[
-48 + 20 = -28
\][/tex]
So, the final result is:
[tex]\[
f(3) = -28
\][/tex]
The correct answer is [tex]\(-28\)[/tex].
