College

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

A. -28
B. -13
C. 62
D. 64

Answer :

To find [tex]\( f(3) \)[/tex] for the function [tex]\( f(x) = -5x^2 - x + 20 \)[/tex], we can follow these steps:

1. Substitute 3 for [tex]\( x \)[/tex] in the function:
Start by replacing [tex]\( x \)[/tex] with 3 in the expression [tex]\( f(x) = -5x^2 - x + 20 \)[/tex].

2. Calculate each part of the expression:
- Compute [tex]\((-5)(3)^2\)[/tex]:
[tex]\[ (3)^2 = 9 \][/tex]
[tex]\[ -5 \times 9 = -45 \][/tex]

- Compute [tex]\(-3\)[/tex] (this comes from [tex]\(-1 \times 3\)[/tex]).

- Combine [tex]\(-45\)[/tex] and [tex]\(-3\)[/tex]:
[tex]\[ -45 + (-3) = -48 \][/tex]

- Add 20 to [tex]\(-48\)[/tex] to finish the calculation:
[tex]\[ -48 + 20 = -28 \][/tex]

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

The correct answer is [tex]\(-28\)[/tex].