document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=108293>Question 108293</A>: <I><SPAN STYLE=\"word-break: break-all;\"> sketch the graph of the function. Label the vertex.\r<BR>\n" );
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document.write( "I have no idea what the vertex is\r<BR>\n" );
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document.write( "here is the problem: y=3x^2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #78916 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=78916\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The vertex is the highest or lowest point on the graph. In this case the vertex is the lowest<BR>\n" );
document.write( "point. The vertex will be the lowest point if you have a quadratic equation such as this<BR>\n" );
document.write( "one is AND the sign of the term that contains x^2 is a plus sign.<BR>\n" );
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document.write( "To help you a little, the graph of y = 3x^2 looks like this:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-10%2C10%2C+-10%2C+10%2C+3x%5E2%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-10%2C10%2C+-10%2C+10%2C+3x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Notice that from this graph it looks as if the vertex is at the x, y point (0, 0),<BR>\n" );
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document.write( "If you have a quadratic equation of the form:<BR>\n" );
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document.write( "y = ax^2 + bx + c<BR>\n" );
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document.write( "The vertex will have an x value of -b/2. For this problem, since the equation you were<BR>\n" );
document.write( "given has no term that contains just \"x\", then b must equal zero. (Similarly, there is<BR>\n" );
document.write( "no constant term so \"c\" must also be zero. And when you compare the given equation <BR>\n" );
document.write( "with the quadratic equation you can see that \"a\" must be 3 because the multiplier of the<BR>\n" );
document.write( "x^2 term is 3.)<BR>\n" );
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document.write( "Anyhow, the vertex will occur where x has the value -b/2 and in this problem b is zero<BR>\n" );
document.write( "so the vertex will occur where x = -0/2 = 0.  But if x = 0, we can use the given equation to<BR>\n" );
document.write( "find that:<BR>\n" );
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document.write( "y = 3x^2 = 3(0)^2 = 0.  <BR>\n" );
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document.write( "Since y is zero when x is 0, we know that the vertex is at the point (0,0).<BR>\n" );
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document.write( "Hope this helps you to understand the problem and how you can find the vertex.<BR>\n" );
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