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:
Replace [tex]\( x \)[/tex] with 3 in the expression given for [tex]\( f(x) \)[/tex]:
[tex]\[
f(3) = -5(3)^2 - (3) + 20
\][/tex]
2. Calculate each part of the expression:
- First, compute [tex]\( 3^2 \)[/tex]:
[tex]\[
3^2 = 9
\][/tex]
- Next, compute [tex]\(-5 \times 9\)[/tex]:
[tex]\[
-5 \times 9 = -45
\][/tex]
- Then, handle the [tex]\(-x\)[/tex] part by substituting [tex]\( x = 3 \)[/tex]:
[tex]\[
-3 = -3
\][/tex]
- Finally, add 20:
[tex]\[
20 = 20
\][/tex]
3. Combine all the parts:
Add the results from the above steps together:
[tex]\[
f(3) = -45 - 3 + 20
\][/tex]
4. Perform the addition and subtraction:
[tex]\[
-45 - 3 = -48
\][/tex]
[tex]\[
-48 + 20 = -28
\][/tex]
Therefore, the value of [tex]\( f(3) \)[/tex] is [tex]\(-28\)[/tex].
1. Substitute [tex]\( x = 3 \)[/tex] into the function:
Replace [tex]\( x \)[/tex] with 3 in the expression given for [tex]\( f(x) \)[/tex]:
[tex]\[
f(3) = -5(3)^2 - (3) + 20
\][/tex]
2. Calculate each part of the expression:
- First, compute [tex]\( 3^2 \)[/tex]:
[tex]\[
3^2 = 9
\][/tex]
- Next, compute [tex]\(-5 \times 9\)[/tex]:
[tex]\[
-5 \times 9 = -45
\][/tex]
- Then, handle the [tex]\(-x\)[/tex] part by substituting [tex]\( x = 3 \)[/tex]:
[tex]\[
-3 = -3
\][/tex]
- Finally, add 20:
[tex]\[
20 = 20
\][/tex]
3. Combine all the parts:
Add the results from the above steps together:
[tex]\[
f(3) = -45 - 3 + 20
\][/tex]
4. Perform the addition and subtraction:
[tex]\[
-45 - 3 = -48
\][/tex]
[tex]\[
-48 + 20 = -28
\][/tex]
Therefore, the value of [tex]\( f(3) \)[/tex] is [tex]\(-28\)[/tex].
