document.write( "Question 254211: The vertical height, h, in metres of a golf ball as it travels a horizontal distance, d metres, down the fairway, can be described using a quadratic function. A pro-golfer can drive the ball 300m down the fairway before it lands. If the ball's maximum height was 15m:\r
\n" ); document.write( "\n" ); document.write( "- draw a sketch of the path of the golf ball
\n" ); document.write( "- find the equation of the path of the golf ball
\n" ); document.write( "- determine the two distances down the fairway when the ball is 10m above the ground. Give your answer to the nearest tenth of a metre. \n" ); document.write( "
Algebra.Com's Answer #186709 by ankor@dixie-net.com(22740)\"\" \"About 
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The vertical height, h, in metres of a golf ball as it travels a horizontal distance, d metres, down the fairway, can be described using a quadratic function.
\n" ); document.write( "A pro-golfer can drive the ball 300m down the fairway before it lands. If the ball's maximum height was 15m:
\n" ); document.write( ":
\n" ); document.write( "- draw a sketch of the path of the golf ball
\n" ); document.write( "- find the equation of the path of the golf ball
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\n" ); document.write( "Find the equation using the form ax^2 + bx = y
\n" ); document.write( "Coordinate at it's highest point: 150,15
\n" ); document.write( "a(150^2) + 150b = 15
\n" ); document.write( "22500a + 150 b = 15
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\n" ); document.write( "Coordinate when it strikes the ground: 300,0
\n" ); document.write( "a(300^2) + 300b = 0
\n" ); document.write( "90000a = 300b = 0
\n" ); document.write( ":
\n" ); document.write( "Multiply the 1st equation by 2, subtract the 2nd equation,
\n" ); document.write( "45000a + 300b = 30
\n" ); document.write( "90000a + 300b = 0
\n" ); document.write( "--------------------subtraction eliminates b, find a
\n" ); document.write( "-45000a = 30
\n" ); document.write( "a = \"30%2F%28-45000%29\"
\n" ); document.write( "a = -.00067
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\n" ); document.write( "Find b using the 2nd equation
\n" ); document.write( "90000(-.00076) + 300b = 0
\n" ); document.write( "-60 + 300b = 0
\n" ); document.write( "300b = 60
\n" ); document.write( "b = \"300%2F60\"
\n" ); document.write( "b = +.2
\n" ); document.write( ":
\n" ); document.write( "the equation of the path of the ball: h = -.00067d^2 + .2d
\n" ); document.write( ":
\n" ); document.write( "A graph of this, h = y axis; d = x axis:
\n" ); document.write( "\"+graph%28+300%2C+200%2C+-50%2C+350%2C+-10%2C+25%2C+-.00067x%5E2%2B.2x%29+\"
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\n" ); document.write( "determine the two distances down the fairway when the ball is 10m above the ground.
\n" ); document.write( " -.00067d^2 + .2d = 10
\n" ); document.write( "-.00067d^2 + .2d - 10 = 0
\n" ); document.write( "use the quadratic formula to find d:
\n" ); document.write( "\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"
\n" ); document.write( "In this problem x = d; a = -.00067, b = .2, c = -10
\n" ); document.write( "\"d+=+%28-.2+%2B-+sqrt%28.2%5E2-4%2A-.00067%2A-10+%29%29%2F%282%2A-.00067%29+\"
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\n" ); document.write( "\"d+=+%28-.2+%2B-+sqrt%28.04+-+.0268+%29%29%2F%28-.00134%29+\"
\n" ); document.write( ":
\n" ); document.write( "\"d+=+%28-.2+%2B-+sqrt%28.0132+%29%29%2F%28-.00134%29+\"
\n" ); document.write( "Two solutions
\n" ); document.write( "\"d+=+%28-.2+-+.1149%29%2F%28-.00134%29+\"
\n" ); document.write( "d = \"%28-.3149%29%2F%28-.00134%29\"
\n" ); document.write( "d = 235.0m
\n" ); document.write( "and
\n" ); document.write( "\"d+=+%28-.2+%2B+.1149%29%2F%28-.00134%29+\"
\n" ); document.write( "d = \"%28-.0851%29%2F%28-.00134%29\"
\n" ); document.write( "d = 63.5m
\n" ); document.write( ":
\n" ); document.write( "The ball will be a 10 meters at 63.5m and 235.0m
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