College

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], follow these steps:

1. Substitute [tex]\( x = 3 \)[/tex] into the function.
2. Calculate the expression [tex]\( -5 \times (3)^2 \)[/tex].
- First, square the 3: [tex]\( 3^2 = 9 \)[/tex].
- Then multiply by -5: [tex]\( -5 \times 9 = -45 \)[/tex].

3. Calculate the expression for the linear term: [tex]\( -x \)[/tex].
- Substitute [tex]\( x = 3 \)[/tex]: [tex]\( -3 \)[/tex].

4. Add the constant term 20 to these results.

5. Now put it all together:
- Start with [tex]\(-45\)[/tex] from the squared term.
- Add [tex]\(-3\)[/tex] from the linear term, giving [tex]\(-45 - 3 = -48\)[/tex].
- Finally, add 20: [tex]\(-48 + 20 = -28\)[/tex].

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