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Complete the table.

\begin{tabular}{|c|c|}
\hline
[tex]$f(q) = q^2 - 6q + 8$[/tex] \\
\hline
[tex]$q$[/tex] & [tex]$f(q)$[/tex] \\
\hline
6 & [tex]$\square$[/tex] \\
\hline
8 & [tex]$\square$[/tex] \\
\hline
10 & [tex]$\square$[/tex] \\
\hline
12 & [tex]$\square$[/tex] \\
\hline
\end{tabular}

Sagot :

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.
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