document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1097695>Question 1097695</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In 2011, a mobile phone company made a live-action version of the popular Angry Birds game at a park in Barcelona as part of their marketing campaign. During the game, a player launched a bird to a maximum height of 12 m above ground. The bird landed 16 m away from its launch platform which is located at ground level. Model the bird’s path using a quadratic function f(x), where x is the horizontal displacement of the bird in meters. Assume that the bird was launched from the origin of the Cartesian plane. Express your answer in standard form. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #712182 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=712182\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the vertex form of a quadratic equation is y = a * (x-h)^2 + k\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(h,k) is the vertex of the equation.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you are given that the maximum height is 12 and that the zero crossing points are  x = 0 and x = 12.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this makes the vertex of the quadratic equation equal to (6,12).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "in the equation of y = a * (x-h)^2 + k, replace h with 6 and k with 12 to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "y = a * (x-6)^2 + 12\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the value of y is 0 when x is equal to 0 or x is equal to 12.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "when x = 0, you get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "0 = a * (0-6)^2 + 12 which becomes 0 = a * (-6)^2 + 12 which becomes 0 = 36a + 12.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "solve for a to get a = -1/3.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "when x = 12, you get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "0 = a * (12-6)^2 + 12 which becomes 0 = a * (6)^2 + 12 which becomes 0 = 36a + 12.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "solve fora to get a = -1/3.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the vertex form of the equation becomes y = -1/3 * (x-6)^2 + 12.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the graph of that equation is shown below:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/101601.jpg\" alt=\"$$$\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you can convert this vertex form of the equation into the standard form of the equation by simplifying it.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "start with y = -1/3 * (x-6)^2 + 12<BR>\n" );
document.write( "simplify to get y = -1/3 * (x^2 - 12x + 36) + 12<BR>\n" );
document.write( "simplify further to get y = -1/3 * x^2 + 4x - 12 + 12<BR>\n" );
document.write( "simplify further to get y = -1/3 * x^2 + 4x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that's the standard form of the equation.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the graph of that equation is shown below:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/101602.jpg\" alt=\"$$$\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );