(College Algebra II) 25. (See Week 2 Lecture page "Transformations" for a starting point.

(College Algebra II)

25. (See Week 2 Lecture page "Transformations" for a starting point.)

a. Starting with the expression for the standard parabola

y = x2

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

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