document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=746086>Question 746086</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help solving this Quadratic equation problem. I would appreciate it... If someone who may help walk me through steps to solving this problem. I need to learn this for my final that's coming up. \r<BR>\n" );
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document.write( "[Travel Speed (mph), Braking Distance (ft)]<BR>\n" );
document.write( "[20(mph), 20 (ft)]<BR>\n" );
document.write( "[40(mph), 105 (ft)]<BR>\n" );
document.write( "[60(mph), 300(ft)]\r<BR>\n" );
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document.write( "a)Find a quadratic function that fits the data on the right.<BR>\n" );
document.write( "b) Use the function to estimate the braking distance of a car that travels at 50 mph.<BR>\n" );
document.write( "c) Does it make sense to use this function when speeds are less than 10 mph? Why or why not?\r<BR>\n" );
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document.write( "y=ax^2+bx+c\r<BR>\n" );
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document.write( "[20(mph), 20 (ft)] (20)=a(20)^2+b(20)+C = 20=400a+20b+C<BR>\n" );
document.write( "[40(mph), 105 (ft)](105)=a(40)^2+b(40)+C = 105=1600a+40b+C<BR>\n" );
document.write( "[60(mph), 300(ft)] (300)=a(60)^2+b(60)+C = 300=3600a+60b+C </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #454143 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=454143\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I need help solving this Quadratic equation problem. I would appreciate it... If someone who may help walk me through steps to solving this problem. I need to learn this for my final that's coming up. <BR>\n" );
document.write( "[Travel Speed (mph), Braking Distance (ft)]<BR>\n" );
document.write( "[20(mph), 20 (ft)]<BR>\n" );
document.write( "[40(mph), 105 (ft)]<BR>\n" );
document.write( "[60(mph), 300(ft)] <BR>\n" );
document.write( "a)Find a quadratic function that fits the data on the right.<BR>\n" );
document.write( "b) Use the function to estimate the braking distance of a car that travels at 50 mph.<BR>\n" );
document.write( "c) Does it make sense to use this function when speeds are less than 10 mph? Why or why not? <BR>\n" );
document.write( "y=ax^2+bx+c <BR>\n" );
document.write( "[20(mph), 20 (ft)] (20)=a(20)^2+b(20)+C = 20=400a+20b+C<BR>\n" );
document.write( "[40(mph), 105 (ft)](105)=a(40)^2+b(40)+C = 105=1600a+40b+C<BR>\n" );
document.write( "[60(mph), 300(ft)] (300)=a(60)^2+b(60)+C = 300=3600a+60b+C<BR>\n" );
document.write( "------<BR>\n" );
document.write( "You now have 3 equations with three variables.<BR>\n" );
document.write( "I used the matrix function on my TI-84 to solve that to get:<BR>\n" );
document.write( "a = 0.138<BR>\n" );
document.write( "b = -4<BR>\n" );
document.write( "c = 45<BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "f(x) = 0.138x^2-4x+45<BR>\n" );
document.write( "f(50)= 190 ft.<BR>\n" );
document.write( "f(10)= 18.8 ft<BR>\n" );
document.write( "==================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "==================<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );