# Problem1

Prep Main Page > Web Conference 2 > Sample Problems > Problem 1

```# DESCRIPTION
# Sample problem for WeBWorK PREP workshop
# Model problem:
# Find the equation of the parabola through (0,1), (1,0) and (2,0).
# WeBWorK problem written by Gavin LaRose, <glarose@umich.edu>
# ENDDESCRIPTION

DOCUMENT();

"PGstandard.pl",
"PGchoicemacros.pl",
"MathObjects.pl",
);

############################################################
# problem set-up
Context("Numeric");

# pick a y-intercept, and the two x-intercepts
\$yint = random(1,5,1);
\$xint1 = random(1,3,1);
\$xint2 = \$xint1 + random(1,3,1);

# the parabola is then
\$parab = Compute( "(\$yint/(\$xint1*\$xint2))*(x-\$xint1)*(x-\$xint2)" );

############################################################
# text

TEXT(beginproblem());
Context()->texStrings;
BEGIN_TEXT

Find the equation of the parabola through the points
\((0, \$yint)\), \((\$xint1, 0)\) and \((\$xint2, 0)\).
\$PAR
\(y = \) \{ \$parab->ans_rule(25) \}

END_TEXT
Context()->normalStrings;

############################################################

ANS( \$parab->cmp() );

Context()->texStrings;
SOLUTION(EV3(<<'END_SOLUTION'));
\$PAR SOLUTION \$PAR
Because the \(x\)-intercepts of the parabola are \(x=\$xint1\)
and \(x=\$xint2\), we know the parabola has the form
\[ y = k (x - \$xint1) (x - \$xint2).\]
To find \(k\), we plug in the given \(y\) intercept and solve:
\( \$yint = k (-\$xint1) (-\$xint2) \), so that
\[ y = \$parab. \]

END_SOLUTION
Context()->normalStrings;

ENDDOCUMENT();

# end of problem
############################################################
```