document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=503728>Question 503728</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help, thank you  :)<BR>\n" );
document.write( "The monthly value of a share of ACME Corporation, in dollars, since January 2009 are shown in the table below. The values of the table below model the behavior of a quadratic function when it is graphed.\r<BR>\n" );
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document.write( "Month..........	Share Value (in dollars)<BR>\n" );
document.write( "0......	55<BR>\n" );
document.write( "3......	16<BR>\n" );
document.write( "5......	0<BR>\n" );
document.write( "7......	-8<BR>\n" );
document.write( "9.....	-8<BR>\n" );
document.write( "11....	0<BR>\n" );
document.write( "13....	16<BR>\n" );
document.write( "15.....	40\r<BR>\n" );
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document.write( "1.	Using the table above, find the quadratic equation that represents the monthly value of a share of ACME Corporation since January 2009. Use the variable x to represent the number of months after January 2009 and the variable y to represent the monthly value.<BR>\n" );
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document.write( "Answer Box (Type your work and answer below)<BR>\n" );
document.write( "Hint: Two row values of the table represent the roots of the quadratic equation. Use these values to find the equation \r<BR>\n" );
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document.write( "2.	Find the y-intercept.  Interpret the meaning of the y-intercept in relation to the given real-life scenario. <BR>\n" );
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document.write( "Answer Box (Type your work and answer below)<BR>\n" );
document.write( "Hint: The y intercept is when the graph intersects the y-axis.\r<BR>\n" );
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document.write( "3.	Find the x-intercepts. Interpret the meaning of the x-intercepts in relation to the given real-life scenario.\r<BR>\n" );
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document.write( "Answer Box (Type your work and answer below)<BR>\n" );
document.write( "Hint: The x intercept is when the graph intersects the x-axis.\r<BR>\n" );
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document.write( "4.	From the equation you found in problem 1, what is the concavity of the parabola? How do you know? What is the lowest or maximum monthly value of a share of ACME Corporation and when did that occur?\r<BR>\n" );
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document.write( "Answer Box (Type your work and answer below)<BR>\n" );
document.write( "Hint: Find the vertex of the parabola.  Remember x represents the number of months since January 2009.\r<BR>\n" );
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document.write( "5.	Using the quadratic equation you found in problem 1, predict the value of a share of ACME Corporation in October 2010?\r<BR>\n" );
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document.write( "Answer Box (Type your work and answer below)<BR>\n" );
document.write( "Hint: Remember x represents the number of months since January 2009. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #339435 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=339435\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The monthly value of a share of ACME Corporation, in dollars, since January 2009 are shown in the table below. The values of the table below model the behavior of a quadratic function when it is graphed.<BR>\n" );
document.write( "Month.......... Share Value (in dollars)<BR>\n" );
document.write( "0...... 55<BR>\n" );
document.write( "3...... 16<BR>\n" );
document.write( "5...... 0<BR>\n" );
document.write( "7...... -8<BR>\n" );
document.write( "9..... -8<BR>\n" );
document.write( "11.... 0<BR>\n" );
document.write( "13.... 16<BR>\n" );
document.write( "15..... 40\r<BR>\n" );
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document.write( "1. Using the table above, find the quadratic equation that represents the monthly value of a share of ACME Corporation since January 2009. Use the variable x to represent the number of months after January 2009 and the variable y to represent the monthly value.<BR>\n" );
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document.write( "Note that when x = 5 and x = 11, y = 0, therefore these are the x intercepts<BR>\n" );
document.write( "(as the hint says); derive two factors and use FOIL to create a quadratic equation<BR>\n" );
document.write( "(x-5)*(x-11) = x^2 - 11x - 5x + 55<BR>\n" );
document.write( "y = x^2 - 16x + 55; is the equation<BR>\n" );
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document.write( "2. Find the y-intercept. Interpret the meaning of the y-intercept in relation to the given real-life scenario.<BR>\n" );
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document.write( "The y intercept occurs when x = 0, then y = 55<BR>\n" );
document.write( "This would be the initial value in Jan 2009<BR>\n" );
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document.write( "3. Find the x-intercepts. Interpret the meaning of the x-intercepts in relation to the given real-life scenario.<BR>\n" );
document.write( "From this we have to assume the share value was par (0) in March and June<BR>\n" );
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document.write( "4. From the equation you found in problem 1, what is the concavity of the parabola? How do you know? What is the lowest or maximum monthly value of a share of ACME Corporation and when did that occur?<BR>\n" );
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document.write( "we know from the fact that the coefficient of x^2 is positive, it is concave and has a minimum<BR>\n" );
document.write( "Here is a graph of that equation, you can see for yourself<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-6%2C+20%2C+-30%2C+80%2C+x%5E2-16x%2B55%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-6%2C+20%2C+-30%2C+80%2C+x%5E2-16x%2B55%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "you can see that the min value is in Aug, (x=8), when the value is -9<BR>\n" );
document.write( "which is the vertex, 8,-9<BR>\n" );
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document.write( "5. Using the quadratic equation you found in problem 1, predict the value of a share of ACME Corporation in October 2010?<BR>\n" );
document.write( "Oct 2010, x = 22<BR>\n" );
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document.write( "y = x^2 - 16x + 55<BR>\n" );
document.write( "y = 22^2 - 16(22) + 55<BR>\n" );
document.write( "y = 484 - 352 + 55<BR>\n" );
document.write( "y = 187 in Oct 2010<BR>\n" );
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document.write( "redraw our graph to show this<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-10%2C+30%2C+-100%2C+220%2C+x%5E2-16x%2B55%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-10%2C+30%2C+-100%2C+220%2C+x%5E2-16x%2B55%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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