document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=735418>Question 735418</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A child throws a ball upward from the roof of a house. The tragctory is parabolic, according to the laws of physics. The height the of the ball above the ground, y in meters is given by the quadratic relation<BR>\n" );
document.write( "y=-3x^2+6x+4\r<BR>\n" );
document.write( "\n" );
document.write( "a) How high is the roof of the house where the ball is thrown.<BR>\n" );
document.write( "b)Complete the square to solve the quadratic equation for the exact values of x when y=0<BR>\n" );
document.write( "c) Use the quadratic formula to confirm your answers from part b)<BR>\n" );
document.write( "d) Exactly how far away from the house(horizontally) does the ball hit the ground?<BR>\n" );
document.write( "e) Use your answers from parts b) and c) and determine the horizontal distance from the house when the ball reaches maximum height.<BR>\n" );
document.write( "f) What is the maximum height of the ball? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #449551 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=449551\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A child throws a ball upward from the roof of a house.<BR>\n" );
document.write( " The trajectory is parabolic, according to the laws of physics.<BR>\n" );
document.write( " The height the of the ball above the ground, y in meters is given by the quadratic relation y=-3x^2+6x+4<BR>\n" );
document.write( ":<BR>\n" );
document.write( "a) How high is the roof of the house where the ball is thrown.<BR>\n" );
document.write( "The ball was thrown when x = 0, therefore the roof is 4 meters high<BR>\n" );
document.write( ":<BR>\n" );
document.write( "b)Complete the square to solve the quadratic equation for the exact values of x when y=0<BR>\n" );
document.write( "-3x^2 + 6x + ___ = -4<BR>\n" );
document.write( "Coefficient of x has to be 1, divide equation by -3<BR>\n" );
document.write( "x^2 - 2x + ___ = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F3 ALIGN=MIDDLE  ALT=\"4%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Find the value that completes the square, divide the coefficient of x<BR>\n" );
document.write( " and square it, add to both sides<BR>\n" );
document.write( "x^2 - 2x + 1 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F3 ALIGN=MIDDLE  ALT=\"4%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > + 1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%29%5E2 ALIGN=MIDDLE  ALT=\"%28x-1%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2F3 ALIGN=MIDDLE  ALT=\"7%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Find the square root of both sides<BR>\n" );
document.write( "x - 1 = +/-<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%287%2F3%29 ALIGN=MIDDLE  ALT=\"sqrt%287%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Two solutions<BR>\n" );
document.write( "x = 1 + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%287%2F3%29 ALIGN=MIDDLE  ALT=\"sqrt%287%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ~ 2.53 <BR>\n" );
document.write( "and<BR>\n" );
document.write( "x = 1 - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%287%2F3%29 ALIGN=MIDDLE  ALT=\"sqrt%287%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ~ -.53<BR>\n" );
document.write( ":<BR>\n" );
document.write( "c) Use the quadratic formula to confirm your answers from part b)<BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-6+%2B-+sqrt%286%5E2-4%2A-3%2A4+%29%29%2F%282%2A-3%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-6+%2B-+sqrt%286%5E2-4%2A-3%2A4+%29%29%2F%282%2A-3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You can do the math on this<BR>\n" );
document.write( ": <BR>\n" );
document.write( "d) Exactly how far away from the house(horizontally) does the ball hit the ground?<BR>\n" );
document.write( "Solution 1 above  x ~ 2.53 meters<BR>\n" );
document.write( ":<BR>\n" );
document.write( "e) Use your answers from parts b) and c) and determine the horizontal distance from the house when the ball reaches maximum height.<BR>\n" );
document.write( "That occurs at the axis of symmetry. x = -b/(2a) is the formula for that<BR>\n" );
document.write( "x = -6/(2*-3)<BR>\n" );
document.write( "x = 1 meter horizontally from the house it will be max height<BR>\n" );
document.write( ":<BR>\n" );
document.write( "f) What is the maximum height of the ball?<BR>\n" );
document.write( "y = -3(1^2) + 6(1) + 4<BR>\n" );
document.write( "y = 7 meters max height </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );