1. Lesson 4.2: Graphing Parabolas Using Transformations
y = x2
y = ax2 and y = –ax2

2. Recall…
The graph of y = x2 x y –3 –2 –1 1 2 3 9 4

3. So… to graph, Remember y = x2
Apply the transformation to find the new
vertex. Then, from the vertex, to find
the next points you go:
Over one, up one (12 = 1)
Over two, up four (22 = 4)
Over three, up nine (32 = 9)
Etc…

4. y = ax2 Let’s try another transformation
Please do not share your ideas out loud.
One graph will correctly represent the equation, and one will incorrectly represent the equation.
The dotted line in each graph represents y = x2
Look carefully at the position of the y-values for the corresponding x-values

5. y = 2x2
YES NO

6. y = 3x2
YES NO

7. YES NO

8. YES NO

9. y = 1.5x2
YES NO

10. Think you’ve got it???
Try these 

11. Which graph represents y = 5x2?b
y = x2 a

12. Which graph represents y = 5x2?

13. Which graph represents ?b a
y = x2

14. Which graph represents ?b

15. SUMMARY y = ax2, is called the “Congruent Curve”
Each regular y-value from y = x2 is multiplied by “a”
If a>1 or a<–1, the graph has a vertical stretch (narrows)
If –1<a<1, the graph has a vertical compression (widens)
If a>0 (+ve), the graph opens up
If a<0 (–ve), the graph is reflected in the x-axis and opens down

16. Example 1: y = –2x2 The vertex is at (0, 0)
a=-2: vertical stretch and reflection in the x-axis
Opens down
Each normal y-value is multiplied by -2 x
y=x2 -2 4 -1 1 2
y=-2x2 -8 -2

17. y = –2x2

18. y = –2x2

19. y = –2x2

20. y = –2x2

21. Example 2: y = x2 The vertex is at (0, 0)
a= : vertical compression, opens up
Each normal y-value is multiplied by x
y=x2 -3 9 -2 4 -1 1 2 3
y=2/3x2 6
8/3
2/3

22. y = x2

23. y = x2

24. y = x2

25. y = x2

26. HOMEWORK y = –¾x2 y = 2x2 y = 4x2 y = –½ x2 y = –3x2 y = ¼x2
Graph each of the following using transformations. State the direction of opening
y = –¾x2
y = 4x2
y = –3x2
y = 2x2
y = –½ x2
y = ¼x2