document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=41253>Question 41253</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you please explain to me how you create an equation (function) from looking at a parabola? I can make a parabola from an equation. But not the other way around. I need very easy and explained steps!<BR>\n" );
document.write( "Thanks for your time and effort.<BR>\n" );
document.write( "-C.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #26656 by </B><A HREF=/tutors/aboutme.mpl?userid=psbhowmick><B>psbhowmick(878)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=psbhowmick><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=psbhowmick><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=26656\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Look at the parabola below.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+200%2C300%2C-1%2C7%2C-1%2C19%2C2%2B%28x-3%29%5E2%2C2+%29 ALIGN=MIDDLE  ALT=\"graph%28+200%2C300%2C-1%2C7%2C-1%2C19%2C2%2B%28x-3%29%5E2%2C2+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "At first find the vertex of the parabola from the figure.<BR>\n" );
document.write( "You can easily do this.<BR>\n" );
document.write( "Here the coordinates of the vertex are (3,2).<BR>\n" );
document.write( "Also you can clearly see that the parabola is having an axis parallel to the x-axis.\r<BR>\n" );
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document.write( "If the coordinates of the vertex of a parabola with axis parallel to x-axis be (h,k) then its equation is of the form<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-k+=+4%2Aa%2A%28x-h%29%5E2 ALIGN=MIDDLE  ALT=\"y-k+=+4%2Aa%2A%28x-h%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >__________________(1)\r<BR>\n" );
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document.write( "In this case h = 3, k = 2<BR>\n" );
document.write( "Put this values in equation (1) then you get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-2+=+4%2Aa%2A%28x-3%29%5E2 ALIGN=MIDDLE  ALT=\"y-2+=+4%2Aa%2A%28x-3%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >__________________(2)\r<BR>\n" );
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document.write( "Now, note the coordinates of the point where the parabola cuts one of the coordinate axes.<BR>\n" );
document.write( "Here the parabola cuts the y-axis at (0,11).<BR>\n" );
document.write( "So (0,11) must be a point on the parabola and hence must satisfy its equation.<BR>\n" );
document.write( "Hence x=0 and y=11 satisfies equation (2).<BR>\n" );
document.write( "Therefore, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11-2+=+4%2Aa%2A%280-3%29%5E2 ALIGN=MIDDLE  ALT=\"11-2+=+4%2Aa%2A%280-3%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9+=+4%2Aa%2A3%5E2+=+36a ALIGN=MIDDLE  ALT=\"9+=+4%2Aa%2A3%5E2+=+36a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+1%2F4 ALIGN=MIDDLE  ALT=\"a+=+1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Put <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+1%2F4 ALIGN=MIDDLE  ALT=\"a+=+1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > in equation and get the required equation of the given parabola.<BR>\n" );
document.write( "Here, the equation of the given parabola is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-2+=+%28x-3%29%5E2 ALIGN=MIDDLE  ALT=\"y-2+=+%28x-3%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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