2. (Quadratic Expressions: Completing the Square). Complete the square in each of the following quadratic expressions:
(i) $x^2 - 2x$; (ii) $8x^2 - 7x$; (iii) $3x^2 + x$.
In the following problem you have to make sketches/drawings. The sketches have to be done with your own hand (as it will be the case most
of the time in the future homework assignments). For the problem that follows, and on similar occasions in the future, prepare a sketch, make a
photo of the sketch (e.g. with your smartphone), transfer the graphic file of the photo to your computer, and include in your work (it may be a
good idea to resize your graphic file first, e.g. to decrease both dimensions by some 70-75%, since 'photofiles' tend to be rather big).
A note for LaTeX users: put a command like
\includegraphics[scale=0.5]{mySketch}
in the corresponding cell(s) in a table with the answers to the problem:
$$
\begin{array}{111}
\textbf{{Subproblem}} & \textbf{{Answer(s)}} \\ \hline \hline
... & ... \\
... & \text{(e)} \\
& \includegraphics[scale=0.25]{mySketch} \\ \hline \hline
\end{array}
$$
Understandably, either increase, or decrease the scale to ensure that your sketch fits properly. Notice also that the filename of the graphic file
(mySketch) is given it without extension (such as .jpg, .png, etc.)--it may be helpful in some cases.
