document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=120787>Question 120787</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello, I'm completely lost. Can anyone help me with this. Please provide sources if you can. Thanks\r<BR>\n" );
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document.write( "Using the Library, web resources, and/or other materials, find a real-life application of a quadratic function. State the application, give the equation of the quadratic function, and state what the x and y in the application represent.  Choose at least two values of x to input into your function and find the corresponding y for each.  State, in words, what each x and y means in terms of your real-life application.  Please see the following example. Do not use any version of this example in your own post. You may use other variables besides x and y, such as t and S depicted in the following example.  Be sure to reference all sources using APA style. \r<BR>\n" );
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document.write( "Typing hint:  To type x-squared, use x^2. Do not use special graphs or symbols because they will not appear when pasted to the Discussion Board.\r<BR>\n" );
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document.write( "When thrown into the air from the top of a 50 ft building, a ball’s height, S, at time t can be found by S(t) = -16t^2 + 32t + 50.  When t = 1, s = -16(1)^2 + 32(1) + 50 = 66. This implies that after 1 second, the height of the ball is 66 feet.  When t = 2, s = -16(2)^2 + 32(2) + 50 = 50. This implies that after 2 seconds, the height of the ball is 50 feet.  \r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #88584 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=88584\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Try using Google with search string quaratic function examples.<BR>\n" );
document.write( "Here's a sample:<BR>\n" );
document.write( "Example 6.\r<BR>\n" );
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document.write( "A rancher has 600 meters of fence to enclose a rectangular corral with another fence dividing it in the middle as in the diagram below.\r<BR>\n" );
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document.write( "As indicated in the diagram, the four horizontal sections of fence will each be x meters long and the three vertical sections will each be y meters long.\r<BR>\n" );
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document.write( "The rancher's goal is to use all of the fence and enclose the largest possible area.\r<BR>\n" );
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document.write( "The two rectangles each have area xy, so we have\r<BR>\n" );
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document.write( "total area: A = 2xy.\r<BR>\n" );
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document.write( "There is not much we can do with the quantity A while it is expressed as a product of two variables. However, the fact that we have only 1200 meters of fence available leads to an equation that x and y must satisfy.\r<BR>\n" );
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document.write( "3y + 4x = 1200.\r<BR>\n" );
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document.write( "3y = 1200 - 4x.\r<BR>\n" );
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document.write( "y = 400 - 4x/3.\r<BR>\n" );
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document.write( "We now have y expressed as a function of x, and we can substitute this expression for y in the formula for total area A.\r<BR>\n" );
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document.write( "A = 2xy = 2x (400 -4x/3).\r<BR>\n" );
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document.write( "We need to find the value of x that makes A as large as possible. A is a quadratic function of x, and the graph opens downward, so the highest point on the graph of A is the vertex. Since A is factored, the easiest way to find the vertex is to find the x-intercepts and average.\r<BR>\n" );
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document.write( "2x (400 -4x/3) = 0.\r<BR>\n" );
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document.write( "2x = 0 or 400 -4x/3 = 0.\r<BR>\n" );
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document.write( "x = 0 or 400 = 4x/3.\r<BR>\n" );
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document.write( "x = 0 or 1200 = 4x.\r<BR>\n" );
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document.write( "x = 0 or 300 = x.\r<BR>\n" );
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document.write( "Therefore, the line of symmetry of the graph of A is x = 150, the average of 0 and 300.\r<BR>\n" );
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document.write( "Now that we know the value of x corresponding to the largest area, we can find the value of y by going back to the equation relating x and y.\r<BR>\n" );
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document.write( "y = 400 - 4x/3 = 400 -4(150)/3 = 200.\r<BR>\n" );
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