Let's evaluate the function step-by-step to find [tex]\( f(2) \)[/tex] for the given function [tex]\( f(x) = 2x^2 - 3x + 7 \)[/tex].
Given:
[tex]\[
f(x) = 2x^2 - 3x + 7
\][/tex]
Step-by-Step Evaluation:
1. Substitute [tex]\( x = 2 \)[/tex] into the function:
[tex]\[
f(2) = 2(2)^2 - 3(2) + 7
\][/tex]
2. Evaluate the exponent:
[tex]\[
(2)^2 = 4
\][/tex]
So, the expression becomes:
[tex]\[
f(2) = 2(4) - 3(2) + 7
\][/tex]
3. Next, perform the multiplication:
[tex]\[
2(4) = 8 \quad \text{and} \quad 3(2) = 6
\][/tex]
Now the expression is:
[tex]\[
f(2) = 8 - 6 + 7
\][/tex]
4. Finally, perform the addition and subtraction:
[tex]\[
8 - 6 = 2
\][/tex]
[tex]\[
2 + 7 = 9
\][/tex]
Therefore, the value of the function when [tex]\( x = 2 \)[/tex] is:
[tex]\[
f(2) = 9
\][/tex]
Thus, the answer is [tex]\( 9 \)[/tex].
