QUESTION. Find the equation for the parabola shown below.

In this example we expect students to know that the two -intercepts
and formulates the quadratic equation
,
and then identify from the third point (for which the vertex is a good choice).
Here we will create any number of different problems by changing
the values , and .
We can also form incorrect answers
such as
,
, and
.
The following `thisquiz.tex` in ``Quiz 1'' illustrates this point,
and realizes it in Maxima-embedded L^{A}TEX document.

\textsc{Question.} Find the equation for the parabola shown below. \maximacode pick([list]) := block([i], i:random(length(list))+1, return(list[i])); a: pick(-2,1/2); x0: pick(-2,0,1); x1: pick(2,3,4); \endmaximacode \begin{center} \maximaplot [a*(x-x0)*(x-x1),x0-1,x1+1] \endmaximaplot \end{center} \begin{enumerate} \item \maxima expand(a*(x-x0)*(x-x1)) \endmaxima \item \maxima expand(-a*(x-x0)*(x-x1)) \endmaxima \item \maxima expand((x-x0)*(x-x1)) \endmaxima \item \maxima expand(-(x-x0)*(x-x1)) \endmaxima \end{enumerate}

Maxima code, a set of maxima expressions, is placed between
`\maximacode`

and `\endmaximacode`

.
In a similar manner a single maxima expression is placed
between `\maxima`

and `\endmaxima`

.
While the maxima code in the first control sequence
has no output,
the maxima expression in the second one
is replaced by the math mode `$ output $`

and the TEX-mathmode output will be inserted.
In either case
if we run latex with `qgmax.sty`,
it shows no effect of Maxima evaluation.

`\maximacode`

maxima code;

.........

maxima code;

`\endmaximacode`

`\maxima`

maxima expression`\endmaxima`

Plotting is controlled by
`\maximaplot`

and `\endmaximaplot`

.
The maxima expressions in this control sequence
is first evaluated by Maxima, and passed onto `gnuplot`.

```
````\maximaplot`

[f(x), x-axis lower limit, x-axis upper limit]

```
````\endmaximaplot`

The comma-separated values ``f(x)'', ``x-axis lower limit'', and ``x-axis upper limit'' are Maxima expression, not allowed to contain commas (``,'') themselves. Other form of control sequence may be chosen from one of the following:

[f(x), x-axis lower limit, x-axis upper limit, y-axis lower limit, y-axis upper limit]

[parametric, lower end of t, upper end of t, f(t) in x-axis, g(t) in y-axis, .....]

[parametric, lower end of t, upper end of t, xrange, x-axis lower limit, x-axis upper limit, f(t) in x-axis, g(t) in y-axis, .....]

[parametric, lower end of t, upper end of t, xrange, x-axis lower limit, x-axis upper limit, yrange, y-axis lower limit, y-axis upper limit, f(t) in x-axis, g(t) in y-axis, .....]

We created a page ``Quiz 1'' for the above example, and linked it as follows:

\subsection{[../Quiz_1/quiz.cgi]Quiz 1}

Note that the path to this page is `/MATHGO/Guide_to_GO/thispage/`

and Quiz 1 is placed under `/MATHGO/Guide_to_GO/Quiz_1/`

.
We have the relative path `../Quiz_1`

to access `thisquiz.tex`.
The perl CGI script `quiz.cgi` will evaluate
`thisquiz.tex` with Maxima, generate HTML, and display it in the window.

Department of Mathematics