document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=448887>Question 448887</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The path traveled by a ball hit into the air can be modeled with the quadratic function, y = -0.042x^+5x, where x is the distance in yards from the point it was hit and y is the height the ball reached in feet.  Assuming that the ground is level. <BR>\n" );
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?\r<BR>\n" );
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document.write( "Please help me with this problem as I am getting a negative figure for the height.  There is something I am not doing correct.\r<BR>\n" );
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document.write( "Thank you.  I look forward for your assistance with this problem. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #308827 by </B><A HREF=/tutors/aboutme.mpl?userid=htmentor><B>htmentor(1343)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=htmentor><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=htmentor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=308827\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> y = -0.042x^2+5x [you left out the 2]<BR>\n" );
document.write( "a) The maximum height reached will be the height at which dy/dx = 0<BR>\n" );
document.write( "dy/dx = 0 = (2)(-0.042)x + 5<BR>\n" );
document.write( "Solve for x:<BR>\n" );
document.write( "0 = -0.084x + 5<BR>\n" );
document.write( "x = 59.52 ft. along the ground.<BR>\n" );
document.write( "Therefore, the maximum height is:<BR>\n" );
document.write( "y = -0.042*(59.52)^2 + 5*59.52 = 148.81 ft.<BR>\n" );
document.write( "b) We need to set y=0 and solve for x:<BR>\n" );
document.write( "0 = -0.042x^2 + 5x<BR>\n" );
document.write( "0 = x(-0.042x + 5)<BR>\n" );
document.write( "This gives x = 0 [the starting point]<BR>\n" );
document.write( "and x = -5/-0.042 = 119.05 ft.<BR>\n" );
document.write( "The graph is below:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-200%2C200%2C-200%2C200%2Cx%2A%28-0.042x%2B5%29%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-200%2C200%2C-200%2C200%2Cx%2A%28-0.042x%2B5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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