Discover the answers you need at Westonci.ca, where experts provide clear and concise information on various topics. Join our platform to connect with experts ready to provide precise answers to your questions in various areas. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.

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.