document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=442622>Question 442622</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1)Find the equation of the parabloa with points (5,0) and (6,10).<BR>\n" );
document.write( "2)Find the equation of the parabola with points (1,5) and (2,10).\r<BR>\n" );
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document.write( "*Please explain step by step.\r<BR>\n" );
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document.write( "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 #305329 by </B><A HREF=/tutors/aboutme.mpl?userid=swincher4391><B>swincher4391(1107)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=swincher4391><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=swincher4391><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=305329\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Since we know that it passes through the point (5,0), then (x-5) is a linear factor.\r<BR>\n" );
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document.write( "x-5 |  ax^2 + bx +5\r<BR>\n" );
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document.write( "So, dx-1 must be the other factor.\r<BR>\n" );
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document.write( "Since 10 = (6-5)(6d-1), then 10 = 1(6d-1) , so d = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=expr%2811%2F6%29 ALIGN=MIDDLE  ALT=\"expr%2811%2F6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "(x-5)((11/6)x-1) = 4/3x^2 - 20/3x +2x -10\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=expr%2811%2F6%29x%5E2+-+55%2F6x+-x+%2B5+=++expr%2811%2F6%29x%5E2+-+expr%2861%2F6%29x+%2B5 ALIGN=MIDDLE  ALT=\"expr%2811%2F6%29x%5E2+-+55%2F6x+-x+%2B5+=++expr%2811%2F6%29x%5E2+-+expr%2861%2F6%29x+%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So our answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=expr%2811%2F6%29x%5E2+-+expr%2861%2F6%29x+%2B+5+ ALIGN=MIDDLE  ALT=\"expr%2811%2F6%29x%5E2+-+expr%2861%2F6%29x+%2B+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "For the second one:<BR>\n" );
document.write( "a(1^2) + b(1) + c = 5<BR>\n" );
document.write( "a(2^2) + b(2) + c = 10<BR>\n" );
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document.write( "Since  4a + 2b +c = 10<BR>\n" );
document.write( "and     a + b + c = 5\r<BR>\n" );
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document.write( "3a + b + 0c = 5<BR>\n" );
document.write( "0a  -2b -3c = -10<BR>\n" );
document.write( "2a  +0b -2c = -15\r<BR>\n" );
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document.write( "add equations 1 and 3 together to get \r<BR>\n" );
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document.write( "5a + b -2c = -10\r<BR>\n" );
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document.write( "Notice 2b + 3c = 10\r<BR>\n" );
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document.write( "Then 5a + 3b + c = 0\r<BR>\n" );
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document.write( "Recognize that a+b+c = 5  and 3a+b = 5\r<BR>\n" );
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document.write( "Then a+b+c = 3a +b.  Meaning 2a =c.\r<BR>\n" );
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document.write( "Then 2a -2c = -15\r<BR>\n" );
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document.write( "c - 2c = -15    -c = -15  so c =15.\r<BR>\n" );
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document.write( "Remember that 2b + 3c = 10\r<BR>\n" );
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document.write( "2b + 45 = 10\r<BR>\n" );
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document.write( "2b = -35\r<BR>\n" );
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document.write( "b = -35/2\r<BR>\n" );
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document.write( "Remember 3a + b = 5.\r<BR>\n" );
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document.write( "3a -35/2 = 5\r<BR>\n" );
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document.write( "6a - 35 = 10\r<BR>\n" );
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document.write( "6a = 45\r<BR>\n" );
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document.write( "a = 45/6  or 15/2\r<BR>\n" );
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document.write( "So our parabola is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=expr%2815%2F2%29x%5E2+-expr%2835%2F2%29x+%2B+15 ALIGN=MIDDLE  ALT=\"expr%2815%2F2%29x%5E2+-expr%2835%2F2%29x+%2B+15\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Wow that was a toughy!\r<BR>\n" );
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document.write( "Hope this helped!\r<BR>\n" );
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document.write( " </SPAN>\n" );
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