Answer :
To find [tex]\( f(3) \)[/tex] for the function [tex]\( f(x) = -5x^2 - x + 20 \)[/tex], follow these steps:
1. Substitute [tex]\( x \)[/tex] with 3 in the function:
Start with the expression for [tex]\( f(x) \)[/tex]:
[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 [tex]\( 3^2 \)[/tex]:
[tex]\[
3^2 = 9
\][/tex]
3. Multiply [tex]\(-5\)[/tex] by the result from step 2:
[tex]\[
-5 \times 9 = -45
\][/tex]
4. Simplify the expression:
Substitute [tex]\(-45\)[/tex] back into the equation:
[tex]\[
f(3) = -45 - 3 + 20
\][/tex]
5. Perform the addition and subtraction:
First, add [tex]\(-45\)[/tex] and [tex]\(-3\)[/tex]:
[tex]\[
-45 - 3 = -48
\][/tex]
Then, add 20:
[tex]\[
-48 + 20 = -28
\][/tex]
Thus, the value of [tex]\( f(3) \)[/tex] is [tex]\(-28\)[/tex].
1. Substitute [tex]\( x \)[/tex] with 3 in the function:
Start with the expression for [tex]\( f(x) \)[/tex]:
[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 [tex]\( 3^2 \)[/tex]:
[tex]\[
3^2 = 9
\][/tex]
3. Multiply [tex]\(-5\)[/tex] by the result from step 2:
[tex]\[
-5 \times 9 = -45
\][/tex]
4. Simplify the expression:
Substitute [tex]\(-45\)[/tex] back into the equation:
[tex]\[
f(3) = -45 - 3 + 20
\][/tex]
5. Perform the addition and subtraction:
First, add [tex]\(-45\)[/tex] and [tex]\(-3\)[/tex]:
[tex]\[
-45 - 3 = -48
\][/tex]
Then, add 20:
[tex]\[
-48 + 20 = -28
\][/tex]
Thus, the value of [tex]\( f(3) \)[/tex] is [tex]\(-28\)[/tex].
