document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=855009>Question 855009</A>: <I><SPAN STYLE=\"word-break: break-all;\"> ok so I got a question today in math foundations 20... I have to sketch a graph of a quadratic equation but I don't have a equation he gave me just information. I only know the axis of symmetry, x=3 the vertex is (3,5)  and finally the y-intercept = (0,8) I only got that no equation how to I graph that? and what would the equation be? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #515022 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=515022\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Understand the standard form for a quadratic (or at least a parabolic) equation.<BR>\n" );
document.write( "<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;\" >;<BR>\n" );
document.write( "vertex is (h,k), and this occurs on the symmetry axis (for a parabola).<BR>\n" );
document.write( "The factor, a, is information about stretching or shrinking, in this form, vertically.  The form shown has a vertical symmetry axis.  \r<BR>\n" );
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document.write( "According to what you are given, you can use that data to fill the standard form equation.  If symmetry axis is x=3, then the parabola opens either upward or downward and the vertex is on this axis.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=a%28x-3%29%5E2%2B5 ALIGN=MIDDLE  ALT=\"y=a%28x-3%29%5E2%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and use the given y-intercept to help find a.<BR>\n" );
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document.write( "First, solve for a.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%28x-3%29%5E2=y-5 ALIGN=MIDDLE  ALT=\"a%28x-3%29%5E2=y-5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=%28y-5%29%2F%28x-3%29%5E2 ALIGN=MIDDLE  ALT=\"a=%28y-5%29%2F%28x-3%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substitute with (0,8).<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=%288-5%29%2F%280-3%29%5E2 ALIGN=MIDDLE  ALT=\"a=%288-5%29%2F%280-3%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=3%2F%289%29 ALIGN=MIDDLE  ALT=\"a=3%2F%289%29\"   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%2F3 ALIGN=MIDDLE  ALT=\"a=1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-<BR>\n" );
document.write( "EQUATION:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=%281%2F3%29%2A%28x-3%29%5E2%2B5%29 ALIGN=MIDDLE  ALT=\"highlight%28y=%281%2F3%29%2A%28x-3%29%5E2%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The parabola is vertical, has a minimum, vertex of (3,5); the coefficient on the leading term came from knowing the y intercept.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-5%2C15%2C-5%2C15%2C%281%2F3%29%28x-3%29%5E2%2B5%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-5%2C15%2C-5%2C15%2C%281%2F3%29%28x-3%29%5E2%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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