document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=348281>Question 348281</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. Given the coordinates of (10,4) and (40,4) lie on the parabola, at what x-coordinate must the vertex lie?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #248986 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=248986\">put this solution on YOUR website!</A><BR><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. Given the coordinates of (10,4) and (40,4) lie on the parabola, <BR>\n" );
document.write( "at what x-coordinate must the vertex lie?<BR>\n" );
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document.write( "What the question wants you to notice is the symmetry of the two<BR>\n" );
document.write( "given points.  They are both at y = 4 and separated by (40-10) = 30<BR>\n" );
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document.write( "The symmetry line is half between 40 and 10; that is 25.<BR>\n" );
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document.write( "So the x-coordinate of the vertex is x = 25.<BR>\n" );
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document.write( "Check it out:<BR>\n" );
document.write( "y = -0.01x^2 + 0.5x<BR>\n" );
document.write( "a = -0.01 ; b = 0.5<BR>\n" );
document.write( "--<BR>\n" );
document.write( "-b/2a = -0.5/(2*-0.01) = 0.5/0.02 = 25<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "==============  </SPAN>\n" );
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