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 #425322 by </B><A HREF=/tutors/aboutme.mpl?userid=MRperkins><B>MRperkins(300)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MRperkins><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=MRperkins><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=425322\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> email me and I will work this one out with you in an online whiteboard.<BR>\n" );
document.write( "http://www.scribblar.com/mg9yqg9\r<BR>\n" );
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document.write( "Basically, we are dealing with a quadratic function.  Generally, that will involve using the \"vertex form\"<BR>\n" );
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document.write( "so, we know that there is a maximum of y=35.  what, in the formula, is the y value of the vertex of the parabola?  (b)<BR>\n" );
document.write( "Since the y values are the same on the given points, then the axis of symmetry is in the middle of them (2+10)/2  or 6.  that is the h value of the vertex.  If they were not the same y values, then we could still find the h value, but it would be more complicated:<BR>\n" );
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document.write( "***alternative way to find h value Start***<BR>\n" );
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document.write( "so we can insert that into the formula:  y=a(x-h)^2+35<BR>\n" );
document.write( "we also know two points that work.  enter the first point and you get 3=a(2-h)^2+35 <BR>\n" );
document.write( "foil (2-h)^2 to get h^2-4h+4, <BR>\n" );
document.write( "solve for \"a\"<BR>\n" );
document.write( "a=-32/(h^2-4h+4)<BR>\n" );
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document.write( "now plug the other point into y=a(x-h)^2+35<BR>\n" );
document.write( "and you get 3=a(10-h)^2+35<BR>\n" );
document.write( "subtract 35 from both sides<BR>\n" );
document.write( "-32=a(10-h)^2<BR>\n" );
document.write( "substitute -32/(h^2-4h+4) from the first equation in for a in the second equation.<BR>\n" );
document.write( "You get:<BR>\n" );
document.write( "-32=(-32(10-h)^2)/(h^2-4h+4)<BR>\n" );
document.write( "reduce the -32's and move the h^2-4h+4 to the left<BR>\n" );
document.write( "reduce to find the h value.<BR>\n" );
document.write( "h=6<BR>\n" );
document.write( "***alternative way to find h value Stop***<BR>\n" );
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document.write( "so now you have y=a(x-6)^2+35<BR>\n" );
document.write( "use one of the points for the x and y value to find \"a\"<BR>\n" );
document.write( "3=a(4)^2+35<BR>\n" );
document.write( "-32/16=a<BR>\n" );
document.write( "a=-2<BR>\n" );
document.write( "so <BR>\n" );
document.write( "y=-2(x-6)^2+35 </SPAN>\n" );
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