document.write( "Question 390217: Ushna sits by the lake and throws a stone by it. The path of the stone is described by the equation h = 22t - 5t^2 where h is the height of the stone in metres at t seconds after it had been thrown. By drawing a suitable graph, find the time taken for each stone to reach:
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Algebra.Com's Answer #276649 by ewatrrr(24785) $\"\"$ $\"About$

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document.write( "Hi
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document.write( "h = 22t - 5t^2   Path of the stone is a parabola:
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document.write( "I. with y-intercept at Pt(0,0)
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document.write( "II.  Opening downward (Note: negative coefficient for the x^2 term)
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document.write( "Note: the vertex form of a parabola,  where(h,k) is the vertex
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document.write( "h = 22t - 5t^2 completing square to find the vertex
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document.write( "h = -5(t^2 - 22/5)
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document.write( "h = -5[(t - 11/5)-121/25]
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document.write( "h = -5( t - 11/5)^2 + 121/5  
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document.write( "Vertex (maximum point) is ( 11/5,121/5)or(2.2,24.2) 
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document.write( "Line of symmetry for this parbola being the perpendicular line x = 2.2
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document.write( "a) time to reach the maximum height is 2.2 sec
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document.write( "b) time to reach the surface of the lake: 0 = t(-5t + 22)  t = 22/5 = 4.4 sec
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document.write( "Sketching the graph to see the path the stone thrown takes:
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document.write( "I. Plot the Points: y-intercept Pt(0,0), vertex (2.2,24.2)
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document.write( "II. draw the vertical axis of symmetry  x = 2.2 and then Plot Pt(4.4,0)
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document.write( "III. Sketch the parabola opening downward using the axis of symmetry as a reference
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