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------------------------------------------------ Given the function [tex]f(x)=-5x^2-x+20[/tex], find [tex]f(3)[/tex].

A. [tex]\(-28\)[/tex]
B. [tex]\(-13\)[/tex]
C. 62
D. 64

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].