document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=171023>Question 171023</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi! I need to determine the equation of a parabola in the form y-k=a(x-h)^2\r<BR>\n" );
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document.write( "I am given 2 points on the graph (0,6) and (14,0)<BR>\n" );
document.write( "I am given Part of V (9,k)\r<BR>\n" );
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document.write( "I have tried so many things, but nothing is even close to what it should be and I am ending up just writing the question over and over and now I am fully frustrated. I know I have to use both points given in order to get \"a\" and \"k\" and I probably have to substitute or eliminate but with two unknowns I have no idea how to go about it!<BR>\n" );
document.write( "Any help would be seriously appreciated! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #126735 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=126735\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> determine the equation of a parabola in the form y-k=a(x-h)^2<BR>\n" );
document.write( "I am given 2 points on the graph (0,6) and (14,0)<BR>\n" );
document.write( "I am given Part of V (9,k); I assume this means h=9<BR>\n" );
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document.write( "Two equations:<BR>\n" );
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document.write( "0,6:<BR>\n" );
document.write( "6 - k = a(0 - 9)^2<BR>\n" );
document.write( "6 - k = 81a<BR>\n" );
document.write( "or<BR>\n" );
document.write( "81a + k = 6<BR>\n" );
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document.write( "14, 0<BR>\n" );
document.write( "0 - k = a(14-9)^2<BR>\n" );
document.write( "0 - k = a(5)^2<BR>\n" );
document.write( "25a + k = 0<BR>\n" );
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document.write( "Eliminate k, find a<BR>\n" );
document.write( "81a + k = 6<BR>\n" );
document.write( "24a + k = 0<BR>\n" );
document.write( "-------------subtraction eliminates k<BR>\n" );
document.write( "56a = 6<BR>\n" );
document.write( "a = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2F56 ALIGN=MIDDLE  ALT=\"6%2F56\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F28 ALIGN=MIDDLE  ALT=\"3%2F28\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Find k using 25a + k = 0<BR>\n" );
document.write( "25*(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F28 ALIGN=MIDDLE  ALT=\"3%2F28\"   DISABLED_style= \"max-width:90%; height:auto;\" >) + k = 0<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=75%2F28 ALIGN=MIDDLE  ALT=\"75%2F28\"   DISABLED_style= \"max-width:90%; height:auto;\" > + k = 0<BR>\n" );
document.write( "k = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-75%2F28 ALIGN=MIDDLE  ALT=\"-75%2F28\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The equation:<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F28 ALIGN=MIDDLE  ALT=\"3%2F28\"   DISABLED_style= \"max-width:90%; height:auto;\" >(x - 9)^2 - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=75%2F28 ALIGN=MIDDLE  ALT=\"75%2F28\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Plots this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-5%2C+20%2C+-4%2C+10%2C+%283%2F28%29%28x-9%29%5E2+-+%2875%2F28%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Looks about right </SPAN>\n" );
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