1. 1.6 Using Multiple Transformations to graph quadratic equations

2. When graphing a quadratic function we can apply the transformations to the key points of But after yesterday maybe you noticed that the vertex is easy to move left or right and never gets effected by the stretch or compression factor.
Always stretch or compress the parabola first!

3. -10 -5 5 10 15
-15 X Y 5 3 1
The “STEP PATTERN” of is “1, 3, 5” and it is the step pattern that changes when the parabola is stretched or compressed!

4. Graph This is a vertical stretch by a factor of 3 so we multiply the step pattern by 3
1 , 3 , 5 x3
3 , 9 , 15

5. -10 -5 5 10 15
-15 X Y 15 9 3

6. X-2 Graph reflect in the x-axis stretch by a factor of 2
shift the parabola right 5
shift the parabola up 3
We can graph it by moving the vertex right 5 and up 3 and using the step pattern to draw the other key points
1 , 3 , 5
X-2
-2 , -6 , -10

7. -10 -5 5 10 15
-15 X Y -2 -6
-10

8. Graph
stretch by a factor of 3
shift the parabola left 1
shift the parabola down 7

9. -10 -5 5 10 15
-15 X Y

10. Graph
reflect in the x-axis
compress by a factor of 0.5
shift the parabola right 8
shift the parabola up 6

11. -10 -5 5 10 15
-15 X Y

12. Graph
reflect in the x-axis
stretch by a factor of 2
shift the parabola left 4
shift the parabola up 5

13. -10 -5 5 10 15
-15 X Y

14. Graph
compress by a factor of
shift the parabola right 2
shift the parabola down 5

15. -10 -5 5 10 15
-15 X Y

16. Homework:
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