document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=151404>Question 151404</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How would I go about writing the quadratic function, in (standard) form, which has a vertex of (-6, 2) and passes through (5, 12)?\r<BR>\n" );
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document.write( "The standard form is y= a(x-h)^2+k , so i would put -6 as h and 2 as k but from there I am stuck. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #111294 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=111294\">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=y=+a%28x-h%29%5E2%2Bk ALIGN=MIDDLE  ALT=\"y=+a%28x-h%29%5E2%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=+a%28x-%28-6%29%29%5E2%2B2 ALIGN=MIDDLE  ALT=\"y=+a%28x-%28-6%29%29%5E2%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=-6 ALIGN=MIDDLE  ALT=\"h=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=2 ALIGN=MIDDLE  ALT=\"k=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=+a%28x%2B6%29%5E2%2B2 ALIGN=MIDDLE  ALT=\"y=+a%28x%2B6%29%5E2%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-%28-6%29 ALIGN=MIDDLE  ALT=\"x-%28-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B6 ALIGN=MIDDLE  ALT=\"x%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since the quadratic passes through (5, 12), this means that if you plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5 ALIGN=MIDDLE  ALT=\"x=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, you will get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=12 ALIGN=MIDDLE  ALT=\"y=12\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So we can plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5 ALIGN=MIDDLE  ALT=\"x=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=12 ALIGN=MIDDLE  ALT=\"y=12\"   DISABLED_style= \"max-width:90%; height:auto;\" > to solve for \"a\"\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12=+a%285%2B6%29%5E2%2B2 ALIGN=MIDDLE  ALT=\"12=+a%285%2B6%29%5E2%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5 ALIGN=MIDDLE  ALT=\"x=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=12 ALIGN=MIDDLE  ALT=\"y=12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12=+a%2811%29%5E2%2B2 ALIGN=MIDDLE  ALT=\"12=+a%2811%29%5E2%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12=+a%28121%29%2B2 ALIGN=MIDDLE  ALT=\"12=+a%28121%29%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square 11 to get 121\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12=+121a%2B2 ALIGN=MIDDLE  ALT=\"12=+121a%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10=+121a ALIGN=MIDDLE  ALT=\"10=+121a\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 2 from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2F121=+a ALIGN=MIDDLE  ALT=\"10%2F121=+a\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 121.\r<BR>\n" );
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document.write( "So the value of \"a\" is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=10%2F121 ALIGN=MIDDLE  ALT=\"a=10%2F121\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This means that the equation is \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=+%2810%2F121%29%28x%2B6%29%5E2%2B2 ALIGN=MIDDLE  ALT=\"y=+%2810%2F121%29%28x%2B6%29%5E2%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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