document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1129340>Question 1129340</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The fuel efficiency for a certain midsize car is given by<BR>\n" );
document.write( "E(v) = &#8722;0.016v2 + 1.376v + 3.8<BR>\n" );
document.write( "where <BR>\n" );
document.write( "E(v)<BR>\n" );
document.write( " is the fuel efficiency in miles per gallon for a car traveling v miles per hour.<BR>\n" );
document.write( "(a) What speed will yield the maximum fuel efficiency? Round to the nearest mile per hour.______mph<BR>\n" );
document.write( "(b) What is the maximum fuel efficiency for this car? Round to the nearest mile per gallon.____mpg </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #745898 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=745898\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> E(v) = -0.016v^2 + 1.376v + 3.8<BR>\n" );
document.write( ":<BR>\n" );
document.write( "this is the equation of a parabola that curves downward<BR>\n" );
document.write( ":<BR>\n" );
document.write( "velocity is plotted along the x-axis and fuel efficiency is plotted along the y-axis<BR>\n" );
document.write( ":<BR>\n" );
document.write( "here is a graph of E(v)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-20%2C+100%2C+-20%2C+40%2C+-0.016x%5E2+%2B1.376x+%2B3.8%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-20%2C+100%2C+-20%2C+40%2C+-0.016x%5E2+%2B1.376x+%2B3.8%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "from the graph, we see that the coordinates of the vertex will give us the answers to the questions a and b<BR>\n" );
document.write( ":<BR>\n" );
document.write( "a. The speed(v) that will yield the maximum fuel efficiency is found from the formula<BR>\n" );
document.write( ":<BR>\n" );
document.write( "v = -b/2a, where b and a are from the general form for a quadratic<BR>\n" );
document.write( ":<BR>\n" );
document.write( "ax^2 +bx +c<BR>\n" );
document.write( ":<BR>\n" );
document.write( "v = -1.376/(2(-0.016)) = 43<BR>\n" );
document.write( ":<BR>\n" );
document.write( "*******************************************<BR>\n" );
document.write( "speed for maximum fuel efficiency is 43 mph<BR>\n" );
document.write( "*******************************************<BR>\n" );
document.write( ":<BR>\n" );
document.write( "b.  substitute for v in the equation<BR>\n" );
document.write( ":<BR>\n" );
document.write( "E(v) = -0.016v^2 + 1.376v + 3.8<BR>\n" );
document.write( ":<BR>\n" );
document.write( "E(v) = -0.016(43)^2 + 1.376(43) + 3.8 = 33.384 is approximately 33<BR>\n" );
document.write( ":<BR>\n" );
document.write( "****************************************************************<BR>\n" );
document.write( "The maximum fuel efficiency for the car is 33 miles per gallon<BR>\n" );
document.write( "****************************************************************<BR>\n" );
document.write( ":<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );