To solve for [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. First, calculate [tex]\( (4)^2 \)[/tex]:
[tex]\[
(4)^2 = 16
\][/tex]
3. Next, multiply this result by 2:
[tex]\[
2 \cdot 16 = 32
\][/tex]
So, the term [tex]\( 2(4)^2 \)[/tex] evaluates to 32.
4. Now calculate the product of -6 and 4:
[tex]\[
-6 \cdot 4 = -24
\][/tex]
5. Add the results together:
[tex]\[
32 + (-24) + 17
\][/tex]
6. Simplify:
First, [tex]\( 32 + (-24) \)[/tex] is [tex]\( 32 - 24 \)[/tex], which is:
[tex]\[
32 - 24 = 8
\][/tex]
Then add 17:
[tex]\[
8 + 17 = 25
\][/tex]
So, [tex]\( f(4) = 25 \)[/tex].
