document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1146110>Question 1146110</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write an equation for the parabola in standard form. Use a graphing utility to graph the equation and verify your result.<BR>\n" );
document.write( "f(x) = \r<BR>\n" );
document.write( "\n" );
document.write( "Point: (0,7)<BR>\n" );
document.write( "Vertex:(-3,-2) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #767402 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=767402\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "As in the response from the other tutor, a vertex at (-3,-2) means the equation is of the form<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-%28-2%29+=+a%28x-%28-3%29%29%5E2 ALIGN=MIDDLE  ALT=\"y-%28-2%29+=+a%28x-%28-3%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "or<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B2+=+a%28x%2B3%29%5E2 ALIGN=MIDDLE  ALT=\"y%2B2+=+a%28x%2B3%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "or<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+a%28x%2B3%29%5E2-2 ALIGN=MIDDLE  ALT=\"y+=+a%28x%2B3%29%5E2-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Then here is a different way to determine the value of the constant a to complete the equation.<br><BR>\n" );
document.write( "Note that the constant a determines how steep the parabola is.<br><BR>\n" );
document.write( "Then note that the given point on the parabola is 3 units to the right of the vertex and 9 units up from the vertex.<br><BR>\n" );
document.write( "Then, since 9 is 3^2, you know the constant a is 1, so the equation is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28x%2B3%29%5E2-2 ALIGN=MIDDLE  ALT=\"y+=+%28x%2B3%29%5E2-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28x%5E2%2B6x%2B9%29-2 ALIGN=MIDDLE  ALT=\"y+=+%28x%5E2%2B6x%2B9%29-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+x%5E2%2B6x%2B7 ALIGN=MIDDLE  ALT=\"y+=+x%5E2%2B6x%2B7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Let's look again at this method for determining the value of the constant a in the equation.<br><BR>\n" );
document.write( "Suppose the given point were (1,6).<br><BR>\n" );
document.write( "That point is 4 to the right of the vertex and 8 units up from the vertex.<br><BR>\n" );
document.write( "Since 4^2 is 16 and the point is only 8 units up from the vertex, the value of the constant a is 8/16 = 1/2.<br><BR>\n" );
document.write( "And one more example, to help you try to see how this method works.<br><BR>\n" );
document.write( "This time the given point is (-1,10).  That point is 2 to the right and 12 up from the vertex.  Since 2^2 is 4, the value of the constant a is 12/4 = 3. </SPAN>\n" );
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