Sure! Let’s complete the table step-by-step.
We need to evaluate the function [tex]\( f(q) = q^2 - 6q + 8 \)[/tex] for the given values of [tex]\( q \)[/tex].
Here are the steps for each [tex]\( q \)[/tex]:
1. For [tex]\( q = 6 \)[/tex]:
We substitute [tex]\( q = 6 \)[/tex] into the function [tex]\( f(q) \)[/tex]:
[tex]\[
f(6) = 6^2 - 6 \cdot 6 + 8 = 36 - 36 + 8 = 8
\][/tex]
So, [tex]\( f(6) = 8 \)[/tex].
2. For [tex]\( q = 8 \)[/tex]:
We substitute [tex]\( q = 8 \)[/tex] into the function [tex]\( f(q) \)[/tex]:
[tex]\[
f(8) = 8^2 - 6 \cdot 8 + 8 = 64 - 48 + 8 = 24
\][/tex]
So, [tex]\( f(8) = 24 \)[/tex].
3. For [tex]\( q = 10 \)[/tex]:
We substitute [tex]\( q = 10 \)[/tex] into the function [tex]\( f(q) \)[/tex]:
[tex]\[
f(10) = 10^2 - 6 \cdot 10 + 8 = 100 - 60 + 8 = 48
\][/tex]
So, [tex]\( f(10) = 48 \)[/tex].
4. For [tex]\( q = 12 \)[/tex]:
We substitute [tex]\( q = 12 \)[/tex] into the function [tex]\( f(q) \)[/tex]:
[tex]\[
f(12) = 12^2 - 6 \cdot 12 + 8 = 144 - 72 + 8 = 80
\][/tex]
So, [tex]\( f(12) = 80 \)[/tex].
Now, let’s complete the table with these values:
[tex]\[
\begin{array}{|c|c|}
\hline
q & f(q) \\
\hline
6 & 8 \\
\hline
8 & 24 \\
\hline
10 & 48 \\
\hline
12 & 80 \\
\hline
\end{array}
\][/tex]
This completes the table.
