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.