Reference no: EM131130023

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.