document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=56231>Question 56231</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0534403654/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> The path traveled by a golf ball hit with a 9-iron can be modeled with the quadratic function, y = -0.042x(squared) + 5x, where x is the distance in yards from the point it was hite and y is the height of the golf ball in feet. Assume that the ground is level.\r<BR>\n" );
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document.write( "a. Find the maximum height reached by the ball.<BR>\n" );
document.write( "b. How far from where it was hit does the ball hit the ground? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #38139 by </B><A HREF=/tutors/aboutme.mpl?userid=funmath><B>funmath(2933)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=funmath><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=38139\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The path traveled by a golf ball hit with a 9-iron can be modeled with the quadratic function, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-0.042x%5E2%2B5x ALIGN=MIDDLE  ALT=\"y=-0.042x%5E2%2B5x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, where x is the distance in yards from the point it was hite and y is the height of the golf ball in feet. Assume that the ground is level.<BR>\n" );
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document.write( "a. Find the maximum height reached by the ball.<BR>\n" );
document.write( "The y value of the vertex is the maximum height the ball.  We can find the x value of the vertex with the formula:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=-b%2F2a%29 ALIGN=MIDDLE  ALT=\"highlight%28x=-b%2F2a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  The b and a we get from the standard form of a parabola: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=ax%5E2%2Bbx%2Bc ALIGN=MIDDLE  ALT=\"y=ax%5E2%2Bbx%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Our a=-0.042 and out b=5.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-%285%29%2F%282%28-0.042%29%29=59.5238 ALIGN=MIDDLE  ALT=\"x=-%285%29%2F%282%28-0.042%29%29=59.5238\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Subtstitute that value into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-0.042x%5E2%2B5x ALIGN=MIDDLE  ALT=\"y=-0.042x%5E2%2B5x\"   DISABLED_style= \"max-width:90%; height:auto;\" > to find the maximum height.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-0.042%2859.5238%29%5E2%2B5%2859.5238%29 ALIGN=MIDDLE  ALT=\"y=-0.042%2859.5238%29%5E2%2B5%2859.5238%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Plug that into your calculator and you'll find the maximum height to be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=148.81ft%29 ALIGN=MIDDLE  ALT=\"highlight%28y=148.81ft%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "b. How far from where it was hit does the ball hit the ground?<BR>\n" );
document.write( "The x-intercepts represent the position of the ball.  Let y=0, factor and solve for x.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=-0.042x%5E2%2B5x ALIGN=MIDDLE  ALT=\"0=-0.042x%5E2%2B5x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=x%28-0.42x%2B5%29 ALIGN=MIDDLE  ALT=\"0=x%28-0.42x%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x=0 is the starting position. <BR>\n" );
document.write( "-0.42x+5=0<BR>\n" );
document.write( "-0.42x=-5<BR>\n" );
document.write( "-0.42x/-0.42=-5/-0.42<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=199.05ft%29 ALIGN=MIDDLE  ALT=\"highlight%28x=199.05ft%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is where it lands.<BR>\n" );
document.write( "Happy Calculating!!! </SPAN>\n" );
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