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y = x 2

y = 2 x 2. (2,8). y = x 2. (2,4). Consider dilating the graph of y = x 2. y. 15. by a factor of 2 from the x -axis. 10. The point ( x , y ) maps onto the point ( x , 2 y ). 5. . (2, 8). e.g. (2, 4). x. -3. -2. -1. 0. 1. 2. 3. y = 3 x 2. (2,12). y = x 2. (2,4).

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y = x 2

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  1. y = 2x2 (2,8) y = x2 (2,4) Consider dilating the graph of y = x2 y 15 by a factor of 2 from the x-axis. 10 The point (x, y) maps onto the point (x, 2y). 5  (2, 8) e.g. (2, 4) x -3 -2 -1 0 1 2 3

  2. y = 3x2 (2,12) y = x2 (2,4) Consider dilating the graph of y = x2 y 15 by a factor of 3 from the x-axis. 10 The point (x, y) maps onto the point (x, 3y). 5  (2, 12) e.g. (2, 4) x -3 -2 -1 0 1 2 3

  3. y = x2 (2,4) y = 0.5x2 (2,2) Consider dilating the graph of y = x2 y 15 by a factor of 0.5 from the x-axis. 10 The point (x, y) maps onto the point (x, 0.5y). 5  (2, 2) e.g. (2, 4) x -3 -2 -1 0 1 2 3

  4. x x A dilation of factor a from the x-axistransforms the graph of y = f(x)to that of y = af(x). (x, y)  (x, ay) A dilation factor greater than 1 ‘stretches’ the graph ‘away from’ the x-axis. A dilation factor less than 1 ‘shrinks’ the graph ‘towards’ the x-axis.

  5. y = x2 (1,1) y = 0.25x2 (2,1) Consider dilating the graph of y = x2 y 15 by a factor of 2 from the y-axis. 10 The point (x, y) maps onto the point (2x, y). 5  (2, 1) e.g. (1, 1) x -3 -2 -1 0 1 2 3

  6. y = 4x2 y = x2 (1,4) (2,4) Consider dilating the graph of y = x2 y 15 by a factor of 0.5 from the y-axis 10 The point (x, y) maps onto the point (0.5x, y). 5  (1, 4) e.g. (2, 4) x -3 -2 -1 0 1 2 3

  7. A dilation of factor a from the y-axistransforms the graph of y = f(x)to that of y = f(). y y (x, y)  (ax, y) A dilation factor greater than 1 ‘stretches’ the graph ‘away from’ the y-axis. A dilation factor less than 1 ‘shrinks’ the graph ‘towards’ the y-axis.

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