The Java applet example To obtain this problem
(1 pt)
The graph above represents the function
where a and b are parameters.
For each value of a find the value of
b which makes the graph just touch the x-axis.
if a= 0.5 then
if a= 2.5 then
if a= 0 then
Does this relationship between a and b specify b as a function of a? (Yes or No)
Does this relationship between a and b specify a as a function of b? (Yes or No)
Write a formula for calculating this value of b from a .
b =
Enter this code
DOCUMENT();
loadMacros(PG.pl,
PGbasicmacros.pl,
PGchoicemacros.pl,
PGanswermacros.pl
);
TEXT(beginproblem());
$javaApplet = <<EOF;
< applet code="mathbeans.SliderGraphApplet.class"
archive="/applets/mathbeans.jar" codebase="../classes/" width=480
height=380>
< PARAM NAME="variable1" VALUE="a">
< PARAM NAME="variable2" VALUE="b">
< param name="function" value="x^2 +a*x +b">
< param name="limits" value="-2 2 -9 9">
</applet>
< H6><A HREF="http://math.hws.edu/mathbeans/applets/index.html">mathbean
applet from David Ecks </A> </H6>
EOF
TEXT(MODES(
TeX => " \fbox{ The java applet was displayed here}",
Latex2HTML => "\begin{rawhtml} $javaApplet \end{rawhtml}",
HTML_tth => $javaApplet,
HTML => $javaApplet,
));
$a1= random(-3,3,.5);
$a2= random(-3,3,.5);
$a3= random(-3,3,.5);
$b1 =($a1/2)**2;
ANS( num_cmp( $b1, reltol => 10, format=>'%0.2g'));
ANS( num_cmp( $b2,reltol => 10, format=>'%0.2g'));
ANS( num_cmp( $b3, reltol => 10,format=>'%0.2g'));
BEGIN_TEXT
$PAR The graph above represents the function \[f(x) = x^2 + a x +b \]
where \( a \) and \( b \) are parameters. $PAR
For each value of \( a \) find the value of \( b \) which makes the
graph just touch the x-axis. $BR
if a= $a1 then \{ ans_rule(10) \}$BR
if a= $a2 then \{ ans_rule(10) \}$BR
if a= $a3 then \{ ans_rule(10) \}
$PAR
Does this relationship between a and b specify b as a function of a? \{
ans_rule(4) \} (Yes or No)$BR
Does this relationship between a and b specify a as a function of b? \{
ans_rule(4) \} (Yes or No)$BR
Write a formula for calculating this value of \( b \) from \( a \).$BR b
= \{ ans_rule(40) \}
END_TEXT
ANS(str_cmp('Yes') ); ANS(str_cmp('No') );
ANS(function_cmp( '(a/2)^2', 'a') );
ENDDOCUMENT();
Comments: This problem is just a demo -- it doesn't
actually work if you push the submit answer button. (You can test a
live
version of this problem.)
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