document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1201024>Question 1201024</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The vertex of this parabola is at (1, 2). When the x-value is 0, the y-value is 0. What is the coefficient of the squared term in the equation of this parabola? \r<BR>\n" );
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document.write( "I don't know where or how to start, please help me. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #835263 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=835263\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the vertex form of the equation is y = a * (x-h)^2 + k.<BR>\n" );
document.write( "(h,k) is the vertex.<BR>\n" );
document.write( "when the vertex is (1,2), this becomes y = a * (x-1)^2 + 2<BR>\n" );
document.write( "when x = 0, y = 0.<BR>\n" );
document.write( "therefore you get:<BR>\n" );
document.write( "0 = a * (-1)^2 + 2<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "0 = a + 2<BR>\n" );
document.write( "solve for a to get:<BR>\n" );
document.write( "a = -2<BR>\n" );
document.write( "vertex form of the equation becomes y = -2 * (x-1)^2 + 2.<BR>\n" );
document.write( "looks like the coefficient of the x^2 term is -2<BR>\n" );
document.write( "the standard form of the equation is y = ax^2 + bx + c<BR>\n" );
document.write( "to convert to this form, set y = 0 in the vertex form and solve.<BR>\n" );
document.write( "you get 0 = -2 * (x-1)^2 + 2<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "0 = -2 * (x^2 -2x + 1) + 2<BR>\n" );
document.write( "simpify to get:<BR>\n" );
document.write( "0 = -2*x^2 + 4x -2 + 2<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "0 = -2x^2 + 4x.<BR>\n" );
document.write( "that's the standard form of the equation.<BR>\n" );
document.write( "your solution is that the coefficient of the x^2 term is -2.<BR>\n" );
document.write( "here's the graph.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2023/031604.jpg\">\r<BR>\n" );
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document.write( "both forms of the equation show on the graph.<BR>\n" );
document.write( "they both show the same figure on the graph, indicating that they are equivalent to each other.\r<BR>\n" );
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document.write( "here's a reference.\r<BR>\n" );
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