Answer :
To find [tex]\( f(3) \)[/tex] for the function [tex]\( f(x) = -5x^2 - x + 20 \)[/tex], follow these steps:
1. Substitute 3 into the function: We replace every [tex]\( x \)[/tex] in the function with 3.
[tex]\[
f(3) = -5(3)^2 - 3 + 20
\][/tex]
2. Calculate [tex]\( 3^2 \)[/tex]: Start by calculating the exponent.
[tex]\[
3^2 = 9
\][/tex]
3. Multiply by -5: Next, multiply the result by -5.
[tex]\[
-5 \times 9 = -45
\][/tex]
4. Subtract 3 from -45: Now, subtract 3 from the result.
[tex]\[
-45 - 3 = -48
\][/tex]
5. Add 20: Finally, add 20 to the above result.
[tex]\[
-48 + 20 = -28
\][/tex]
Thus, [tex]\( f(3) = -28 \)[/tex].
1. Substitute 3 into the function: We replace every [tex]\( x \)[/tex] in the function with 3.
[tex]\[
f(3) = -5(3)^2 - 3 + 20
\][/tex]
2. Calculate [tex]\( 3^2 \)[/tex]: Start by calculating the exponent.
[tex]\[
3^2 = 9
\][/tex]
3. Multiply by -5: Next, multiply the result by -5.
[tex]\[
-5 \times 9 = -45
\][/tex]
4. Subtract 3 from -45: Now, subtract 3 from the result.
[tex]\[
-45 - 3 = -48
\][/tex]
5. Add 20: Finally, add 20 to the above result.
[tex]\[
-48 + 20 = -28
\][/tex]
Thus, [tex]\( f(3) = -28 \)[/tex].
