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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. [tex]62[/tex]
D. [tex]64[/tex]

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:
The function is given as [tex]\( f(x) = -5x^2 - x + 20 \)[/tex].
Substitute 3 for [tex]\( x \)[/tex]:
[tex]\( f(3) = -5(3)^2 - 3 + 20 \)[/tex].

2. Calculate [tex]\( 3^2 \)[/tex]:
[tex]\( 3^2 = 9 \)[/tex].

3. Multiply by [tex]\(-5\)[/tex]:
Multiply 9 by [tex]\(-5\)[/tex]:
[tex]\(-5 \times 9 = -45\)[/tex].

4. Add [tex]\(-x\)[/tex]:
Add [tex]\(-3\)[/tex] to the result ([tex]\(-45\)[/tex]):
[tex]\(-45 - 3 = -48\)[/tex].

5. Add 20 to the result:
Finally, add 20 to [tex]\(-48\)[/tex]:
[tex]\(-48 + 20 = -28\)[/tex].

Therefore, [tex]\( f(3) = -28 \)[/tex].

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