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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