document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=169462>Question 169462</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A cannonball fired out to sea from a shore battery follows a parabolic trajectory given by the graph of the equation<BR>\n" );
document.write( "h(x)=10x - 0.01x^2<BR>\n" );
document.write( "where h(x) is the height of the cannonball above the water when it has traveled a horizontal distance of x feet.\r<BR>\n" );
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document.write( "a.) What is the maximum height that the cannonball reaches?<BR>\n" );
document.write( "b.) How far does the cannonball travel horizontally before splashing into the water?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #124934 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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=124934\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> since this is a parabola in the form of ax^2 + bx + c, we can find the x value of the maximum / minimum point by using the formula -b/2a, where b is the coefficient of the x term and a is the coefficient of the x^2 term.<BR>\n" );
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document.write( "a = -.01<BR>\n" );
document.write( "b = 10<BR>\n" );
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document.write( "since a is negative, the graph will be head up and tails down so that the maximum / minimum point will be a maximum point.<BR>\n" );
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document.write( "-b/2a = -(10)/2*(-.01) = (-10)/(-.02) = 10/.02 = 500<BR>\n" );
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document.write( "x = 500 is the x value of the maximum point.<BR>\n" );
document.write( "h(500) will be the y value.<BR>\n" );
document.write( "since h(x) = 10x - .01x^2, then<BR>\n" );
document.write( "h(500) = 10*500 - .01*(500)^2<BR>\n" );
document.write( "simplifying:<BR>\n" );
document.write( "h(500) = 5000 - .01*250000<BR>\n" );
document.write( "h(500) = 5000 - 2500<BR>\n" );
document.write( "h(500) = 2500<BR>\n" );
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document.write( "maximum height will be 2500 feet when the cannon ball has reached a horizontal distance of 500 feet.<BR>\n" );
document.write( "graph of this trajectory looks like this:<BR>\n" );
document.write( "look below the graph for further comments.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28800%2C800%2C-100%2C1900%2C-1000%2C3000%2C10x-.01x%5E2%29 ALIGN=MIDDLE  ALT=\"graph%28800%2C800%2C-100%2C1900%2C-1000%2C3000%2C10x-.01x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "the x intercepts are when the graph of the equation crosses the x axis.<BR>\n" );
document.write( "these are determined by setting the quadratic equation equal to 0.<BR>\n" );
document.write( "10x - .01x^2 = 0<BR>\n" );
document.write( "this can be factored to become:<BR>\n" );
document.write( "x (10-.01x) = 0<BR>\n" );
document.write( "x = 0<BR>\n" );
document.write( "or<BR>\n" );
document.write( "10-.01x = 0<BR>\n" );
document.write( "solving for x in equation:<BR>\n" );
document.write( "10 - .01x = 0<BR>\n" );
document.write( "add .01x to both sides of equation:<BR>\n" );
document.write( "10 = .01x<BR>\n" );
document.write( "divide both sides of equation by .01:<BR>\n" );
document.write( "10/.01 = x<BR>\n" );
document.write( "simplify:<BR>\n" );
document.write( "1000 = x<BR>\n" );
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document.write( "x intercepts are either<BR>\n" );
document.write( "x = 0<BR>\n" );
document.write( "or<BR>\n" );
document.write( "x = 1000<BR>\n" );
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document.write( "this can be seen from the graph.<BR>\n" );
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document.write( "</TD></TR></TABLE>\n" );