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Alternatively, introduce + - 1 16 1 16 inside the bracket so that equation (iii) becomes: = y - 2 - + - x 2 x 2 1 16 1 16 3 , which gives: = y - - 2 - + x 2 x 2 1 16 1 8 3. This equation can be written in the form = y - 2 - x 1 4 2 25 8 ------- (iv). Using ideas about transformations of graphs of functions, the equation (iv) shows that the graph of = y - - 2 x 2 x 3 has the same shape as the parbabola = y 2 x 2 , because it can be obtained by first translating the curve = y 2 x 2 to the right by 1 4 unit to give the curve = y 2 - x 1 4 2 , and then shifted = 25 8 3 1 8 units down to form the curve = y - 2 - x 1 4 2 25 8 . In particular, the lowest point or vertex of the parabola = y 2 x 2 moves from the origin to the point , 1 4 - 25 8 . The parabola = y 2 x 2 is obtained by scaling the y coordinates of the points on the curve = y x 2 with the factor 2 so that they all move vertically to lie at twice the distance from the x axis, which stretches the graph = y x 2 parallel to the y axis.
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