document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=424415>Question 424415</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1)For each gallon of gas you find you can go 26 miles, if you drive 20mph.  You can go 34 miles if you go 40mph and 32 miles if you go 50mph.  Find a quadratic function that models this data.  What is the best speed to go with this model? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #295889 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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/cgi-bin/show-face.mpl?user=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=295889\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For each gallon of gas you find you can go 26 miles, if you drive 20mph.<BR>\n" );
document.write( " You can go 34 miles if you go 40mph and 32 miles if you go 50mph.<BR>\n" );
document.write( " Find a quadratic function that models this data. <BR>\n" );
document.write( "What is the best speed to go with this model?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Set up a set of coordinates, where x = speed, y = miles traveled on 1 gal of gas<BR>\n" );
document.write( "Using the form y = ax^2 + bx (we don't need c here) find a and b<BR>\n" );
document.write( ":<BR>\n" );
document.write( "\"you can go 26 miles, if you drive 20mph.\"<BR>\n" );
document.write( "x=20, y=26<BR>\n" );
document.write( "20^2a + 20b = 26<BR>\n" );
document.write( "400a + 20b = 26<BR>\n" );
document.write( ":<BR>\n" );
document.write( "\"32 miles if you go 50mph.\"<BR>\n" );
document.write( "x=50, y=32<BR>\n" );
document.write( "50^2a + 50b = 32<BR>\n" );
document.write( "2500a + 50b = 32<BR>\n" );
document.write( ":<BR>\n" );
document.write( "multiply the first equation by 2.5, subtract from the above equation<BR>\n" );
document.write( "2500a + 50b = 32<BR>\n" );
document.write( "1000a + 50b = 65<BR>\n" );
document.write( "------------------Subtraction eliminates b, find a<BR>\n" );
document.write( "1500a = -33<BR>\n" );
document.write( "a = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-33%29%2F1500 ALIGN=MIDDLE  ALT=\"%28-33%29%2F1500\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a = -.022<BR>\n" );
document.write( "Find b, using the 1st equation<BR>\n" );
document.write( "400(-.022) + 20b = 26<BR>\n" );
document.write( "-8.8 + 20b =  26<BR>\n" );
document.write( "20b = 26 + 8.8<BR>\n" );
document.write( "20b = 34.8<BR>\n" );
document.write( "b = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=34.8%2F20 ALIGN=MIDDLE  ALT=\"34.8%2F20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "b = 1.74<BR>\n" );
document.write( ":<BR>\n" );
document.write( "The equation we are looking for:<BR>\n" );
document.write( "y = -.022x^2 + 1.74x<BR>\n" );
document.write( ";<BR>\n" );
document.write( "Check this when,\"You can go 34 miles if you go 40mph\"<BR>\n" );
document.write( "Replace x with 40 mph<BR>\n" );
document.write( "y = -.022(40^2) + 1.74(40)<BR>\n" );
document.write( "y = -35.2 + 69.6<BR>\n" );
document.write( "y = 34.4 not quite 34 but the equation is very close<BR>\n" );
document.write( ":<BR>\n" );
document.write( "\"What is the best speed to go with this model?\"<BR>\n" );
document.write( "Find the axis symmetry for this equation for max distance ; x=-b/(2a)<BR>\n" );
document.write( "In this equation; a=-.022; b=1.74<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1.74%29%2F%282%2A-.022%29 ALIGN=MIDDLE  ALT=\"%28-1.74%29%2F%282%2A-.022%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1.74%29%2F%28-.044%29 ALIGN=MIDDLE  ALT=\"%28-1.74%29%2F%28-.044%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = +39.545 mph, the speed for max distance </SPAN>\n" );
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