math problem

 9. 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 = -2(x + 4)

 2 – 1 

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.