Hello loesThe graph of is the graph of shifted to the right units.

The graph of is the graph of stretched parallel to the -axis with factor .

The graph of is the graph of shifted downwards units.

Put these three facts together, and you can describe how the graph of is obtained from the graph of .

Where is the vertex of ? So where will it end up when you apply all three of these transformations?what are the co-ordinates of the vertex of the parabola?

The -intercepts are the values of that satisfy .what are the x-intercepts and the y-intercepts of the parabola?

The -intercept is the value of when .

What is the image set for ? What will happen to this set when the transformations are applied?what is the image set of the function in interval notation?

Grandad