Answer :
To find [tex]\( f(3) \)[/tex] for the function [tex]\( f(x) = -5x^2 - x + 20 \)[/tex], we need to substitute [tex]\( x = 3 \)[/tex] into the function and simplify.
Here's a step-by-step solution:
1. Substitute [tex]\( x = 3 \)[/tex] into the function:
[tex]\[
f(3) = -5(3)^2 - (3) + 20
\][/tex]
2. Calculate [tex]\( 3^2 \)[/tex]:
[tex]\[
3^2 = 9
\][/tex]
3. Multiply by -5:
[tex]\[
-5 \times 9 = -45
\][/tex]
4. Add [tex]\(-3\)[/tex] (since we replace [tex]\(-x\)[/tex] with [tex]\(-3\)[/tex]):
[tex]\[
-45 - 3 = -48
\][/tex]
5. Add 20:
[tex]\[
-48 + 20 = -28
\][/tex]
After substituting and simplifying, we find that [tex]\( f(3) = -28 \)[/tex].
So, the correct answer is [tex]\(-28\)[/tex].
Here's a step-by-step solution:
1. Substitute [tex]\( x = 3 \)[/tex] into the function:
[tex]\[
f(3) = -5(3)^2 - (3) + 20
\][/tex]
2. Calculate [tex]\( 3^2 \)[/tex]:
[tex]\[
3^2 = 9
\][/tex]
3. Multiply by -5:
[tex]\[
-5 \times 9 = -45
\][/tex]
4. Add [tex]\(-3\)[/tex] (since we replace [tex]\(-x\)[/tex] with [tex]\(-3\)[/tex]):
[tex]\[
-45 - 3 = -48
\][/tex]
5. Add 20:
[tex]\[
-48 + 20 = -28
\][/tex]
After substituting and simplifying, we find that [tex]\( f(3) = -28 \)[/tex].
So, the correct answer is [tex]\(-28\)[/tex].
