document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1027749>Question 1027749</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me and show all steps and work. I am really lost.\r<BR>\n" );
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document.write( "Find the equation of the parabola that contains the points (-1,10),(2,-5)and(3,-18). Once you found the equation, answer the following questions:<BR>\n" );
document.write( "a. Where is the vertex<BR>\n" );
document.write( "b. Is the vertex a maximum or minimum<BR>\n" );
document.write( "c. Where is the focus<BR>\n" );
document.write( "d. Where are the x-intercepts?\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #642991 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=642991\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "A parabola is described by a quadratic function of the form:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y(x)\ =\ ax^2\ +\ bx\ c\">\r<BR>\n" );
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document.write( "Any point on the parabola must be of the form:  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(x,\,y(x)\right)\">\r<BR>\n" );
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document.write( "So if <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (-1,10)\"> is on the graph, it must be true that:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ a(-1)^2\ +\ b(-1)\ +\ c\ =\ 10\">\r<BR>\n" );
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document.write( "Which is to say:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ a\ -\ b\ +\ c\ =\ 10\">\r<BR>\n" );
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document.write( "Similarly:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 4a\ +\ 2b\ +\ c\ =\ -5\">\r<BR>\n" );
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document.write( "and\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 9a\ +\ 3b\ +\ c\ =\ -18\">\r<BR>\n" );
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document.write( "Solve the 3X3 system to find the coefficients of the desired function.\r<BR>\n" );
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document.write( "Once you have the function, the vertex is at the point <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(-\frac{b}{2a},\,y\left(-\frac{b}{2a}\right)\right)\">\r<BR>\n" );
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document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large a\ >\ 0\">, the parabola opens upward and the vertex is a minimum.  If <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large a\ <\ 0\">, the parabola opens downward and the vertex is a maximum.  If <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large a\"> IS zero, then you don't have a parabola.  Check the solution to your 3X3 system, because you have made an error in this case.\r<BR>\n" );
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document.write( "Given that the vertex is at <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (h,k)\">, the focus is at <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(h,k\ +\ \frac{1}{4a}\right)\">, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large a\"> being the lead coefficient of your function.\r<BR>\n" );
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document.write( "For the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\">-intercepts, set your function equal to zero and solve for the two roots.  Given correct algebra and arithmetic, your quadratic equation should factor, though it might be easier to just use the quadratic formula.\r<BR>\n" );
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document.write( "Good luck.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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