High School

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Given the function [tex]f(x)=9x^2+27x+2[/tex], find [tex]f(2)[/tex].

A. [tex]f(2)=65[/tex]
B. [tex]f(2)=76[/tex]
C. [tex]f(2)=92[/tex]
D. [tex]f(2)=94[/tex]

Answer :

Sure! Let's find [tex]\( f(2) \)[/tex] for the function [tex]\( f(x) = 9x^2 + 27x + 2 \)[/tex] step-by-step.

1. Substitute [tex]\( x = 2 \)[/tex] into the function:
[tex]\[
f(2) = 9(2)^2 + 27(2) + 2
\][/tex]

2. Calculate [tex]\( (2)^2 \)[/tex]:
[tex]\[
(2)^2 = 4
\][/tex]

3. Multiply by 9:
[tex]\[
9 \times 4 = 36
\][/tex]

4. Calculate [tex]\( 27 \times 2 \)[/tex]:
[tex]\[
27 \times 2 = 54
\][/tex]

5. Add these results together with the constant term 2:
[tex]\[
36 + 54 + 2 = 92
\][/tex]

So, the value of [tex]\( f(2) \)[/tex] is [tex]\(\boxed{92}\)[/tex], which corresponds to option C.

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