Answer :
To find the value of the function [tex]\( f(x) = -5x^2 - x + 20 \)[/tex] at [tex]\( x = 3 \)[/tex], we need to substitute [tex]\( 3 \)[/tex] into the function and simplify.
1. Start with the function: [tex]\( f(x) = -5x^2 - x + 20 \)[/tex].
2. Substitute [tex]\( x = 3 \)[/tex] into the function:
[tex]\[
f(3) = -5(3)^2 - (3) + 20
\][/tex]
3. Calculate [tex]\( 3^2 \)[/tex]:
[tex]\[
3^2 = 9
\][/tex]
4. Substitute this value back into the equation:
[tex]\[
f(3) = -5(9) - 3 + 20
\][/tex]
5. Multiply [tex]\(-5\)[/tex] by [tex]\(9\)[/tex]:
[tex]\[
-5 \times 9 = -45
\][/tex]
6. Update the equation with this result:
[tex]\[
f(3) = -45 - 3 + 20
\][/tex]
7. Perform the subtraction [tex]\(-45 - 3\)[/tex]:
[tex]\[
-45 - 3 = -48
\][/tex]
8. Finally, add [tex]\(20\)[/tex] to [tex]\(-48\)[/tex]:
[tex]\[
-48 + 20 = -28
\][/tex]
Therefore, the value of [tex]\( f(3) \)[/tex] is [tex]\(-28\)[/tex].
1. Start with the function: [tex]\( f(x) = -5x^2 - x + 20 \)[/tex].
2. Substitute [tex]\( x = 3 \)[/tex] into the function:
[tex]\[
f(3) = -5(3)^2 - (3) + 20
\][/tex]
3. Calculate [tex]\( 3^2 \)[/tex]:
[tex]\[
3^2 = 9
\][/tex]
4. Substitute this value back into the equation:
[tex]\[
f(3) = -5(9) - 3 + 20
\][/tex]
5. Multiply [tex]\(-5\)[/tex] by [tex]\(9\)[/tex]:
[tex]\[
-5 \times 9 = -45
\][/tex]
6. Update the equation with this result:
[tex]\[
f(3) = -45 - 3 + 20
\][/tex]
7. Perform the subtraction [tex]\(-45 - 3\)[/tex]:
[tex]\[
-45 - 3 = -48
\][/tex]
8. Finally, add [tex]\(20\)[/tex] to [tex]\(-48\)[/tex]:
[tex]\[
-48 + 20 = -28
\][/tex]
Therefore, the value of [tex]\( f(3) \)[/tex] is [tex]\(-28\)[/tex].
