Transformations

Starting with the expression for the standard parabola

y = x^2

deduce the sequence of transformations needed to create the graph of the function y=-3(x-3)^2 - 5

Note: For instance, if we were given the function y = -3|x – 4| + 1 we would start with the absolute value function y = |x| and the sequence of transformations would be:

· -  Shift right 4 units, yielding y = |x – 4|

· -  Stretch by a factor of 3, yielding y = 3|x – 4|

· -  Reflect about the x-axis, yielding y = -3|x – 4|

· -  Shift upward 1 unit, yielding y = -3|x – 4| + 1

Graph each transformation in the sequence on the same set of axes.