# 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");
$showPartialCorrectAnswers = 0; # pick a y-intercept, and the two x-intercepts$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
$$y =$$ \{ $parab->ans_rule(25) \} END_TEXT Context()->normalStrings; ############################################################ # answer and solution ANS($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
############################################################