document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1040585>Question 1040585</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi there, I could use your help with the following problem:\r<BR>\n" );
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document.write( "The fuel efficiency F for a particular car is given by:\r<BR>\n" );
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document.write( "F(x) = –.016x^2 + 1.44x + 5.4 \r<BR>\n" );
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document.write( "where x is the speed of the car in miles per hour (mph) and F(x) is the corresponding fuel efficiency in miles per gallon (mpg).\r<BR>\n" );
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document.write( "What is the fuel efficiency if the car’s speed is 20 mph? \r<BR>\n" );
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document.write( "I came up with 34.3024, but I\"m confused on the next question:\r<BR>\n" );
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document.write( "What speed will yield the maximum fuel efficiency? \r<BR>\n" );
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document.write( "any help or guidance would be greatly appreciated! Thank yoU! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #655424 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=655424\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+F%28x%29+=+-.016x%5E2+%2B+1.44x+%2B+5.4+ ALIGN=MIDDLE  ALT=\"+F%28x%29+=+-.016x%5E2+%2B+1.44x+%2B+5.4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(a)<BR>\n" );
document.write( "What is the fuel efficiency if the car’s speed is 20 mph? <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+F%2820%29+=+-.016%2A20%5E2+%2B+1.44%2A20+%2B+5.4+ ALIGN=MIDDLE  ALT=\"+F%2820%29+=+-.016%2A20%5E2+%2B+1.44%2A20+%2B+5.4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+F%2820%29+=+-.016%2A400+%2B+28.8+%2B+5.4+ ALIGN=MIDDLE  ALT=\"+F%2820%29+=+-.016%2A400+%2B+28.8+%2B+5.4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+F%2820%29+=+-6.4+%2B+28.8+%2B+5.4+ ALIGN=MIDDLE  ALT=\"+F%2820%29+=+-6.4+%2B+28.8+%2B+5.4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+F%2820%29+=+27.8+ ALIGN=MIDDLE  ALT=\"+F%2820%29+=+27.8+\"   DISABLED_style= \"max-width:90%; height:auto;\" > mi/gal<BR>\n" );
document.write( "Check my math on this!<BR>\n" );
document.write( "---------------------------<BR>\n" );
document.write( "This is a parabola, so it has either a single maximum or<BR>\n" );
document.write( "a single  minimum.<BR>\n" );
document.write( "The minus sign in front of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2+ ALIGN=MIDDLE  ALT=\"+x%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > term tells me<BR>\n" );
document.write( "this is a maximum<BR>\n" );
document.write( "----------------------<BR>\n" );
document.write( "The formula for the x-value of the vertex ( peak ) is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5Bv%5D+=+-b%2F%282a%29+ ALIGN=MIDDLE  ALT=\"+x%5Bv%5D+=+-b%2F%282a%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > when the form of the equation is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+ax%5E2+%2B+b%2Ax+%2B+c+ ALIGN=MIDDLE  ALT=\"+y+=+ax%5E2+%2B+b%2Ax+%2B+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+-.016+ ALIGN=MIDDLE  ALT=\"+a+=+-.016+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+1.44+ ALIGN=MIDDLE  ALT=\"+b+=+1.44+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5Bv%5D+=+-1.44+%2F+%28+2%2A%28-.016%29+%29+ ALIGN=MIDDLE  ALT=\"+x%5Bv%5D+=+-1.44+%2F+%28+2%2A%28-.016%29+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5Bv%5D+=+1.44+%2F+.032+ ALIGN=MIDDLE  ALT=\"+x%5Bv%5D+=+1.44+%2F+.032+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5Bv%5D+=+45+ ALIGN=MIDDLE  ALT=\"+x%5Bv%5D+=+45+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This says the peak mi/gal occurs when the speed is 45 mi/hr<BR>\n" );
document.write( "----------------------<BR>\n" );
document.write( "Plug this value of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+ ALIGN=MIDDLE  ALT=\"+x+\"   DISABLED_style= \"max-width:90%; height:auto;\" > back into the equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+F%2845%29+=+-.016%2A45%5E2+%2B+1.44%2A45+%2B+5.4+ ALIGN=MIDDLE  ALT=\"+F%2845%29+=+-.016%2A45%5E2+%2B+1.44%2A45+%2B+5.4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+F%2845%29+=+-.016%2A2025+%2B+64.8+%2B+5.4+ ALIGN=MIDDLE  ALT=\"+F%2845%29+=+-.016%2A2025+%2B+64.8+%2B+5.4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+F%2845%29+=+-32.4+%2B+64.8+%2B+5.4+ ALIGN=MIDDLE  ALT=\"+F%2845%29+=+-32.4+%2B+64.8+%2B+5.4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+F%2845%29+=+37.8+ ALIGN=MIDDLE  ALT=\"+F%2845%29+=+37.8+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The maximum fuel efficiency is 37.8 mi/gal<BR>\n" );
document.write( "-------------------------------------<BR>\n" );
document.write( "Here's the plot:<BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+400%2C+400%2C+-10%2C+100%2C+-10%2C+50%2C+-.016%2Ax%5E2+%2B+1.44x+%2B+5.4+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-10%2C+100%2C+-10%2C+50%2C+-.016%2Ax%5E2+%2B+1.44x+%2B+5.4+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );