document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=184560>Question 184560</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I'm can't figure out how to create a quadratic equation out of the vertex and a point that it must pass through. All i've managed so far is some trial and error and come up with this.<BR>\n" );
document.write( "y=2(x+2)²+4<BR>\n" );
document.write( "From the vertex of (-2,4) and passing through (-1,8).<BR>\n" );
document.write( "I have been fiddling around with it and have two ideas how to proceed.<BR>\n" );
document.write( "I could change (x+2) to something else to move it along the x axis or change the first part of it to change the fatness or whichever you want to call it of the parabola.  Regardless i figure there is a better way to do it other then trial and error, if it has been answered before i'm sorry I didn't see it. I'm self taught and this is the first time I really have had any problem. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #138539 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=138539\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If you have three points on a parabola, you can determine the equation of the parabola by substituting the coordinates of your points into:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ Ax^2 + Bx + C = y\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Giving you three simultaneous linear equations that can be solved for the values of the coefficients <i>A</i>, <i>B</i>, and <i>C</i>.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "But you only have two points, namely the vertex and one other point.  However, if you use the properties of symmetry for a parabola, you can easily develop the coordinates of the third point.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Your only problem is that you must decide whether your parabola's axis of symmetry is vertical, giving you an equation where <i>y</i> is defined in terms of <i>x</i>, or whether the axis is horizontal, giving you an equation where <i>x</i> is defined in terms of <i>y</i>.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If (-2, 4) is the vertex and (-1,8) is a point on the parabola with a vertical axis of symmetry, there is another point on the parabola with a <i>y</i> value of 8 and the <i>x</i> value that produces it will be equidistant from the vertex on the other side of the vertex from (-1,8), namely (-3, 8).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If this is the case, then:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 4A - 2B + C = 4 \ \ (-2, 4)\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ A - B + C = 8 \ \ (-1, 8)\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 9A - 3B + C = 8 \ \ (-3, 8)\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Solve this system by your favorite method; either Gaussian Elimination or Cramer's Rule should do.  The solution set will give you the three required coefficients.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If you think your parabola has a horizontal axis, then your third point is (-1, 0), and you will use:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ Ay^2 + By + C = x\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "to set up your three equations.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "In the absence of any evidence as to the orientation of the axis of symmetry, you might consider doing the problem both ways.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
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( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );