document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=521058>Question 521058</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The equation y = 0.5x - .01x^2 represents the parabolic flight of a certain cannonball shot at an angle of 26 degrees with the horizon and an initial velocity of 25 meters per second. In this equation, y is the height of the cannonball, in meters, and the x is the vertical distance traveled, in meters. \r<BR>\n" );
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document.write( "First, Given the points (10,4) abd (40,0) lie on the parabola, at what x-coordinate must the vertex lie?<BR>\n" );
document.write( "- I figured out that it is 25 meters because y = -0.01x^2 + 0.5x. a= -0.01 and b= 0.5. The I plugged it into -b/2a and got x=25. \r<BR>\n" );
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document.write( "Secondly, use the equation and your answer to part one to find the maximum heigth of the baseball. <BR>\n" );
document.write( "- I plugged it into the equation of y = -0.01x^2 + 0.5x. It looked like this <BR>\n" );
document.write( "  y = -0.01(25)^2 + 0.5(25)<BR>\n" );
document.write( "  y= 6.25\r<BR>\n" );
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document.write( "Now, it says to use the point (0,0) and the location of the vertex to find the total horizontal distance that the baseball will travel. Im not sure how to find that. Could you help me?\r<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 #346320 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=346320\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "First let's fix a couple of errors.  In the first place, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\"> doesn't represent the vertical distance traveled.  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\"> is the height and the height is on the vertical axis.  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\"> represents the <i>horizontal</i> distance traveled.  Second, the point <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(10,\,4\right)\"> is on the parabola but the point <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(40,\,0\right)\"> most definately is NOT. <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(40,\,4\right)\"> is on the parabola because <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 0.5(40)\ -\ 0.01(40^2)\ =\ 20\ -\ 16\ =\ 4\">.\r<BR>\n" );
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document.write( "The rest is correct.\r<BR>\n" );
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document.write( "Now, for the last bit.  Parabolas are symmetrical about the axis which is a line through the vertex.  In this case, since the parabola is concave down, the axis is the vertical line <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ =\ 25\">.  Since the parabola is symmetrical, the horizontal distance from the vertex back to the point where the projectile started, namely <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(0,\,0\right)\">, is the same as the horizontal distance from the vertex to the point where the ball hits the ground again (and presumably, for this rather simplistic model anyway, the ball stops).  Since the ball started at a horiziontal distance of 0 and was at the vertex when it reached a horizontal distance of 25, it must have continued for another 25 feet before hitting the ground (0 height) and coming to rest.  Hence, the maximum horizontal travel was 25 + 25 = 50 feet.\r<BR>\n" );
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document.write( "You might care to notice that if you were to set your function equal to zero and solve the quadratic, you would have two roots, namely 0 and 50.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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