To evaluate [tex]\( f(4) \)[/tex] given the function [tex]\( f(x) = 2x^2 - 6x + 17 \)[/tex], follow these steps:
1. Substitute [tex]\( x = 4 \)[/tex] into the function [tex]\( f(x) \)[/tex]:
[tex]\[
f(4) = 2(4)^2 - 6(4) + 17
\][/tex]
2. Calculate [tex]\( (4)^2 \)[/tex]:
[tex]\[
(4)^2 = 16
\][/tex]
3. Multiply [tex]\( 2 \)[/tex] by the result from step 2:
[tex]\[
2 \times 16 = 32
\][/tex]
4. Calculate [tex]\( 6 \times 4 \)[/tex]:
[tex]\[
6 \times 4 = 24
\][/tex]
5. Substitute the results from steps 3 and 4 back into the function:
[tex]\[
f(4) = 32 - 24 + 17
\][/tex]
6. Perform the subtraction [tex]\( 32 - 24 \)[/tex]:
[tex]\[
32 - 24 = 8
\][/tex]
7. Add the result from step 6 to 17:
[tex]\[
8 + 17 = 25
\][/tex]
Therefore, [tex]\( f(4) = 25 \)[/tex].
