document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=687718>Question 687718</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the equation of the parabola that passes through the points (2,3) and (10,3) and has a max value of y=35.\r<BR>\n" );
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document.write( "Can you please help me out? thanks in advance </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #425335 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=425335\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  Find the equation of the parabola that passes through the points (2,3) and (10,3) and has a max value of 35<BR>\n" );
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document.write( "From the two points, 2,3 and 10,3, we know the axis of symmetry is halfway between them and is the x coordinate of the max, so we have a third point, 6,35<BR>\n" );
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document.write( "Using the y = ax^2 + bx + c form we can solve for a, b, c; three equations:<BR>\n" );
document.write( "x=2, y=3<BR>\n" );
document.write( "4a + 2b + c = 3<BR>\n" );
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document.write( "x=6, y=35<BR>\n" );
document.write( "36a + 6b + c = 35 <BR>\n" );
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document.write( "x=10, y=3<BR>\n" );
document.write( "100a + 10b + c = 35<BR>\n" );
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document.write( "Eliminate c<BR>\n" );
document.write( "36a + 6b + c = 35<BR>\n" );
document.write( "4a + 2b + c = 3<BR>\n" );
document.write( "=------------------subtraction eliminates c<BR>\n" );
document.write( "32a + 4b = 32<BR>\n" );
document.write( "Simplify, divide by 4<BR>\n" );
document.write( "8a + b = 8<BR>\n" );
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document.write( "Eliminate c again<BR>\n" );
document.write( "100a + 10b + c = 3<BR>\n" );
document.write( " 36a + 6b + c = 35<BR>\n" );
document.write( "----------------------<BR>\n" );
document.write( "64a + 4b = -32<BR>\n" );
document.write( "Simplify, divide by 4<BR>\n" );
document.write( "16a + b = -8<BR>\n" );
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document.write( "Use these two equations to eliminate b<BR>\n" );
document.write( "16a + b = -8<BR>\n" );
document.write( " 8a + b = 8<BR>\n" );
document.write( "---------------subtracting eliminates b, find a<BR>\n" );
document.write( "8a = -16<BR>\n" );
document.write( "a = -16/8<BR>\n" );
document.write( "a = -2<BR>\n" );
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document.write( "Find b using 8a + b = -8<BR>\n" );
document.write( "8(-2) + b = 8<BR>\n" );
document.write( "b = 8 + 16<BR>\n" );
document.write( "b = 24<BR>\n" );
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document.write( "Find c using 4a + 2b + c = 3<BR>\n" );
document.write( "4(-2) + 2(24) + c = 3<BR>\n" );
document.write( "-8 + 48 + c = 3<BR>\n" );
document.write( "c = 3 - 40<BR>\n" );
document.write( "c = -37<BR>\n" );
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document.write( "The equation: y = -2x^2 + 24x -37 </SPAN>\n" );
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