document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1046925>Question 1046925</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how do i solve for a vertex? when it asks for a Vertex of (0,0) and it is mimnimum?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #662373 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=662373\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Depending how you have the equation,  general form y=ax^2+bx+c or standard form y=a(x-h)^2+k;  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%3E0 ALIGN=MIDDLE  ALT=\"a%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" > will make vertex to be a minimum.  Vertex of (0,0) will make the standard form equation take the format  y=ax^2.  The vertex would be the point,  (h,k).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E2 ALIGN=MIDDLE  ALT=\"y=x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a reference equation for a parabola.  Vertex will be the point  (0,0).  Setup a data table to find some point, graph the points, and sketch this and you will find a graph like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-10%2C10%2C-10%2C10%2Cx%5E2%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-10%2C10%2C-10%2C10%2Cx%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If you shift the graph leftward or rightward, using subtraction of some value h, then in standard form, you would have an equation like <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28x-h%29%5E2 ALIGN=MIDDLE  ALT=\"y=%28x-h%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  This would be a shift TO THE RIGHT, IF <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%3E0 ALIGN=MIDDLE  ALT=\"h%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" >; or a SHIFT TO THE LEFT IF <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%3C0 ALIGN=MIDDLE  ALT=\"h%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  This means that the vertex, still touching the x-axis, will be at  (h,0).<BR>\n" );
document.write( "-<BR>\n" );
document.write( "Imagine that h=5.<BR>\n" );
document.write( "The equation could become <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28x-5%29%5E2 ALIGN=MIDDLE  ALT=\"y=%28x-5%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the graph is this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-10%2C10%2C-10%2C10%2C%28x-5%29%5E2%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-10%2C10%2C-10%2C10%2C%28x-5%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Imagine that h=-2.<BR>\n" );
document.write( "The equation could become <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28x-%28-2%29%29%5E2 ALIGN=MIDDLE  ALT=\"y=%28x-%28-2%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28x%2B2%29%5E2 ALIGN=MIDDLE  ALT=\"y=%28x%2B2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and this shifts the model reference graph two units LEFTWARD, still with vertex touching the x-axis.<BR>\n" );
document.write( "The graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-10%2C10%2C-10%2C10%2C%28x%2B2%29%5E2%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-10%2C10%2C-10%2C10%2C%28x%2B2%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "and vertex is at   (-2,0).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Looking again at standard form, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28x-h%29%5E2%2Bk ALIGN=MIDDLE  ALT=\"y=%28x-h%29%5E2%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and not yet discussing how k value will contribute to the shifting of the graph,  vertex is  (h,k); and if the vertex is (0,0), the Origin, then putting these coordinates values into the standard form model,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28x-0%29%5E2%2B0 ALIGN=MIDDLE  ALT=\"y=%28x-0%29%5E2%2B0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E2 ALIGN=MIDDLE  ALT=\"y=x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "I have used in these examples, a=1. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );