document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=33150>Question 33150</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0534373526/algebrahomeworkh>College Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> A ball is thrown across a playing field. Its path is given by the equation y= -0.005x^2 +x +5, where x is the distance the ball has traveled horizontally, and y is its height above ground level, both measured in feet.\r<BR>\n" );
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document.write( "a. What is the maximum height attained by the ball?\r<BR>\n" );
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document.write( "b. How far has it traveled horizontally when it hits the ground?\r<BR>\n" );
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document.write( "I know this involves vertex and quadratic equations but it doesn't graph right.\r<BR>\n" );
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document.write( "Thank you very much! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #19841 by </B><A HREF=/tutors/aboutme.mpl?userid=mukhopadhyay><B>mukhopadhyay(490)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mukhopadhyay><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=19841\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> y=-0.005x^2+x+5 is a quadratic function representing parabola opening downward.<BR>\n" );
document.write( "The maximum height is reached at its vertex; Hence the y-coordinate of the vertex will give us the required maximum height the ball can attain. <BR>\n" );
document.write( "If there is an x-intercept of a vertex, the larger x-intercept will give us the the distance the ball would travel horizontally when it hits the ground;<BR>\n" );
document.write( "- I am providing the above explanation so that you will not only be able to solve this type of problems, but also be able to develop a concept behind this-......<BR>\n" );
document.write( "x-coordinate of the vertex is attained at -b/2a (for function ax^2+bx+c);<BR>\n" );
document.write( "Here, a=-.005; b=1; Hence x-coordinate of vertex = -1/(2)(-.005) = 1/.01 = 100;<BR>\n" );
document.write( "y-coordinate of the vertex is f(-b/2a)<BR>\n" );
document.write( "= f(100) = -.005(10^4) + 100 + 5 = -50+105 = 55;<BR>\n" );
document.write( "Answer (1): Maximum height the ball can attain is 55 feet;<BR>\n" );
document.write( ".........<BR>\n" );
document.write( "x-intercepts are found by equating f(x) = 0;<BR>\n" );
document.write( "So, -0.005x^2+x+5 = 0<BR>\n" );
document.write( "=> .005x^2-x-5 = 0<BR>\n" );
document.write( "=> 5x^2-1000x-5000 = 0<BR>\n" );
document.write( "=> x^2-200x-1000 = 0<BR>\n" );
document.write( "=> larger x= {-(-200) + Sqrt[(-200)^2-4(1)(-1000)]]/2(1) = [200+sqrt(44000)]/2<BR>\n" );
document.write( "= 100+55sqrt(10);<BR>\n" );
document.write( "Answer (2): The distance the ball would travel horizontally when it hits the ground is 100+55*sqrt(10) feet.<BR>\n" );
document.write( " </SPAN>\n" );
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