Exercise Set 2.1: Transformations of Parabolas Matching. The left-hand column contains equations that represent transformations of y = x2. Match the equations on the left with the description on the right of how to obtain the graph of g from the graph of f . 1. y = (x − 4)2
A. Reflect in the x-axis.
2. y = x2 – 4
B. Shift left 4 units, then reflect in the y-axis.
3. y = x2 + 4 4. y = (x + 4)2 5. y = −x2 6. y = (−x)2
C. Reflect in the x-axis, then shift downward 4 units. D. Shift right 4 units.
(a) Graph each of each of the following functions obtained from the graph of y = x2. (b) Label the x-intercepts (if they exist), the y-intercept, and vertex of the parabola. (c) Determine whether the vertex a maximum or a minimum? 13. y = x2 + 1 14. y = x2 – 3 15. y = (x + 4)2 16. y = (x − 7)2
8. y = ¼x2
E. Shift right 3 units, then reflect in the xaxis, then shift upward 4 units.
9. y = −x2 – 4
F. Shift upward 4 units.
19. y = (x – 3)2 + 3
10. y = (x + 4)2 + 3
G. Reflect in the y-axis.
20. y = (x – 4)2 – 1
7. y = 4x2
11. y = −(x – 3)2 + 4 H. Shift left 4 units, then shift upward 3 units. 12. y = (−x + 4)2 I. Shift left 4 units. J. Shift downward 4 units. K. Stretch vertically by a factor of 4. L. Shrink vertically by a factor of ¼.
17. y = (x + 2)2 – 3 18. y = (x + 4)2 + 2
21. y = −(x + 3)2 – 8 22. y = −(x – 3)2 + 8 23. y = – ¼(x – 2)2 – 5 24. y = 2(x − 5)2 − 7
