High School

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------------------------------------------------ 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 need to substitute 3 into the function wherever there's an [tex]\( x \)[/tex].

Here are the steps to follow:

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

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

3. Calculate the square of 3:
[tex]\[
3^2 = 9
\][/tex]

4. Substitute the result of [tex]\( 3^2 \)[/tex] back into the equation:
[tex]\[
f(3) = -5 \times 9 - 3 + 20
\][/tex]

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

6. Substitute back the result:
[tex]\[
f(3) = -45 - 3 + 20
\][/tex]

7. Add and subtract the remaining numbers:
[tex]\[
-45 - 3 = -48
\][/tex]
[tex]\[
-48 + 20 = -28
\][/tex]

Therefore, [tex]\( f(3) = -28 \)[/tex]. The correct answer is [tex]\(-28\)[/tex].