document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=206447>Question 206447</A>: <I><SPAN STYLE=\"word-break: break-all;\"> what is the equation of a parabola graph?        \r<BR>\n" );
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document.write( "The parabola opens downward.   The vertex is (0,2).  It also has points (-2,-2) and (2,-2) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #156003 by </B><A HREF=/tutors/aboutme.mpl?userid=mickclns><B>mickclns(59)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mickclns><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=156003\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There are several forms in which the equation of a parabola can be written.  One of them is vertex form, because the vertex can be read directly off of it. the form is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+a%28x-h%29%5E2+%2B+k+ ALIGN=MIDDLE  ALT=\"+y+=+a%28x-h%29%5E2+%2B+k+\"   DISABLED_style= \"max-width:90%; height:auto;\" > where (h,k) is the vertex, occasionally written as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+-+k+=+a%28x-h%29%5E2+ ALIGN=MIDDLE  ALT=\"+y+-+k+=+a%28x-h%29%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  If the parabola opens up then a is a positive number, and if the parabola opens down then a is a negative number.<BR>\n" );
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document.write( "If the parabola opens right (a+) or left a-), then the equation would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+a%28y-k%29%5E2+%2Bh+ ALIGN=MIDDLE  ALT=\"+x+=+a%28y-k%29%5E2+%2Bh+\"   DISABLED_style= \"max-width:90%; height:auto;\" > where (h,k) is the vertex,  or  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+-+h+=+%28y+-+k%29%5E2+ ALIGN=MIDDLE  ALT=\"x+-+h+=+%28y+-+k%29%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >. (note the y part is squared and the x part is not)<BR>\n" );
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document.write( "In the case of yours, then you have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+a%28x-0%29%5E2+%2B+2+ ALIGN=MIDDLE  ALT=\"+y+=+a%28x-0%29%5E2+%2B+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and a is negative.  So, how do you find a?  Well, you talk about an equation having points.  That means if you plug the x and the y coordinates of the point into x and y, respectively, the equation you should come out with a true statement/equation.  So, let's take one of the other points (the vertex won't help you find a (Why?) ), how about (2,-2) ... when you plug 2 in for x and -2 in for y, you have:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-2+=+a%282-0%29%5E2+%2B+2+ ALIGN=MIDDLE  ALT=\"+-2+=+a%282-0%29%5E2+%2B+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-4+=+4a+%2B+2+ ALIGN=MIDDLE  ALT=\"+-4+=+4a+%2B+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a=-1 ALIGN=MIDDLE  ALT=\"+a=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So an equation for your parabola is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+-1%28x-0%29%5E2+%2B+2+ ALIGN=MIDDLE  ALT=\"+y+=+-1%28x-0%29%5E2+%2B+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  --  of course the  1 in the -1  and the -0 in the x-0 could be dropped: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+-x%5E2+%2B+2+ ALIGN=MIDDLE  ALT=\"+y+=+-x%5E2+%2B+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "The graph looks like:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28300%2C300%2C-3%2C3%2C-3%2C3%2C-x%5E2+%2B+2%29+ ALIGN=MIDDLE  ALT=\"+graph%28300%2C300%2C-3%2C3%2C-3%2C3%2C-x%5E2+%2B+2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Other forms of the equation are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+ax%5E2+%2B+bx+%2B+c+ ALIGN=MIDDLE  ALT=\"+y+=+ax%5E2+%2B+bx+%2B+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+a%28x-b%29%28x-c%29+ ALIGN=MIDDLE  ALT=\"+y+=+a%28x-b%29%28x-c%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  -  Mick </SPAN>\n" );
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