document.write( "Question 688908: A cannon fires a cannonball whose path is a parabola with vertex
\n" ); document.write( "at the highest point of the path. If the cannonball lands 1600 feet from the
\n" ); document.write( "cannon and the highest point reached is 3200 feet above the ground, find an
\n" ); document.write( "equation for the path of the cannonball. \n" ); document.write( "
Algebra.Com's Answer #425748 by josmiceli(19441)\"\" \"About 
You can put this solution on YOUR website!
You can relate 2 variables- \"+h+\" plotted on
\n" ); document.write( "the vertical axis, and \"+d+\" plotted on the horizontal
\n" ); document.write( "axis. I know that the 2 roots of the equation are:
\n" ); document.write( "\"+d+=+0+\"
\n" ); document.write( "\"+d+=+1600+\"
\n" ); document.write( "This is because \"+d+=+0+\" is where the cannonball is
\n" ); document.write( "fired from and \"+d+=+3200+\" is where it lands.
\n" ); document.write( "----------
\n" ); document.write( "The general form for a parabola is
\n" ); document.write( "\"+h+=+a%2Ad%5E2+%2B+b%2Ad+%2B+c+\"
\n" ); document.write( "You are given 2 points, ( 0,0 ) and ( 1600, 0 )
\n" ); document.write( "(0,0)
\n" ); document.write( "\"+0+=+a%2A0%5E2+%2B+b%2A0+%2B+c+\"
\n" ); document.write( "\"+0+=+c+\"
\n" ); document.write( "So now the equation looks like
\n" ); document.write( "\"+h+=+a%2Ad%5E2+%2B+b%2Ad+\"
\n" ); document.write( "-------------------
\n" ); document.write( "(1600,0)
\n" ); document.write( "\"+0+=+a%2A%281600%29%5E2+%2B+b%2A1600+\"
\n" ); document.write( "\"+a%2A%281600%29%5E2+=+-b%2A1600+\"
\n" ); document.write( "\"+1600a+=+-b+\"
\n" ); document.write( "\"+b+=+-1600a+\"
\n" ); document.write( "----------------
\n" ); document.write( "The vertex is at \"+-b%2F%282a%29%2C+h%5Bmax%5D+\"
\n" ); document.write( "\"+-b%2F%282a%29+=+1600a%2F%282a%29+\"
\n" ); document.write( "\"+-b%2F%282a%29+=+800+\"
\n" ); document.write( "You are given that \"+h%5Bmax%5D+=+3200+\"
\n" ); document.write( "\"+3200+=+a%2A800%5E2+%2B+b%2A800+\"
\n" ); document.write( "\"+4+=+800a+%2B+b+\"
\n" ); document.write( "Since \"+b+=+-1600a+\"
\n" ); document.write( "\"+4+=+800a+-+1600a+\"
\n" ); document.write( "\"+4+=+-800a+\"
\n" ); document.write( "\"+a+=+-1%2F200+\"
\n" ); document.write( "and
\n" ); document.write( "\"+b+=+-1600a+\"
\n" ); document.write( "\"+b+=+-1600%2A%28-1%2F200+%29+\"
\n" ); document.write( "\"+b+=+8+\"
\n" ); document.write( "The equation is:
\n" ); document.write( "\"+h+=+-%281%2F200%29%2Ad%5E2+%2B+8d+\"
\n" ); document.write( "------------------------
\n" ); document.write( "check answer:
\n" ); document.write( "Does it go through (0,0)?
\n" ); document.write( "\"+h+=+-%281%2F200%29%2Ad%5E2+%2B+8d+\"
\n" ); document.write( "\"+0+=+-%281%2F200%29%2A0%5E2+%2B+8%2A0+\"
\n" ); document.write( "\"+0+-+0+\"
\n" ); document.write( "OK
\n" ); document.write( "Does it go through (1600,0)?
\n" ); document.write( "\"+h+=+-%281%2F200%29%2Ad%5E2+%2B+8d+\"
\n" ); document.write( "\"+0+=+-%281%2F200%29%2A1600%5E2+%2B+8%2A1600+\"
\n" ); document.write( "\"+0+=+-2560000%2F200+%2B+12800+\"
\n" ); document.write( "\"++0+=+-12800+%2B12800+\"
\n" ); document.write( "\"+0+=+0+\"
\n" ); document.write( "OK
\n" ); document.write( "Is the vertex at ( 800, 3200 )?
\n" ); document.write( "\"+h+=+-%281%2F200%29%2Ad%5E2+%2B+8d+\"
\n" ); document.write( "\"+3200+=+-%281%2F200%29%2A800%5E2+%2B+8%2A800+\"
\n" ); document.write( "\"+4+=+-%281%2F200%29%2A800+%2B+8+\"
\n" ); document.write( "\"+%281%2F200%29%2A800+=+4+\"
\n" ); document.write( "\"+4+=+4+\"
\n" ); document.write( "OK
\n" ); document.write( "Here's a plot of the parabola.\r
\n" ); document.write( "\n" ); document.write( "\"+graph%28+600%2C+600%2C+-500%2C+1800%2C+-500%2C+3500%2C+-%281%2F200%29%2Ax%5E2+%2B+8x+%29+\"\r
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