High School

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 the value of the function [tex]\( f(x) = -5x^2 - x + 20 \)[/tex] at [tex]\( x = 3 \)[/tex], we substitute [tex]\( 3 \)[/tex] into the function:

1. Start with the function:
[tex]\( f(x) = -5x^2 - x + 20 \)[/tex].

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

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

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

5. Substitute [tex]\(-45\)[/tex] into the expression:
[tex]\( f(3) = -45 - 3 + 20 \)[/tex].

6. Subtract [tex]\(3\)[/tex] from [tex]\(-45\)[/tex]:
[tex]\(-45 - 3 = -48\)[/tex].

7. Add [tex]\(20\)[/tex] to [tex]\(-48\)[/tex]:
[tex]\(-48 + 20 = -28\)[/tex].

So, the value of [tex]\( f(3) \)[/tex] is [tex]\(-28\)[/tex].