Transforming Quadratic Functions
1. Fill in the table and graph f(x) = x2.
x
-3
-2
-1
0
1
2
3
4
y=x2
y
Domain: ________
Range: ________
Describe the transformation of each quadratic function below and sketch
the graph.
2. f(x) = -x2
3. h(x) = (x + 2)2
4. g(x) = (x – 2)2
5. g(x) = x2 + 2
7. f(x) = 2x2
Function:
6. h(x) = x2 – 2
8. g(x) =
1 2
x
2
Effect on graph of parent function
9. f(x) = -x2
_______________________________
10. h(x) = (x + h)2
_______________________________
11. g(x) = (x - h )2
_______________________________
12. h(x) = x2 + k
_______________________________
13. f(x) = x2 – k
_______________________________
14. g(x) = ax2
_______________________________
15. Graph g(x) = -(x – 3)2 + 1
Domain: ________
Range: ________
16. Graph h(x) = 2(x + 4)2 - 2
Domain: ________
Range: ________
Write the equation for each of the following. Start with the graph of f(x) = x².
17. Shift 3 units left, and 6 units down. ________________________
18. Reflect over the x-axis, stretch by a factor of 3. ____________________
19. Shrink by a factor of
1
, shift 3 units right and 2 units up. _______________
2
20. Reflect across the x-axis, stretch by a factor of 2, shifts 2 units to the right,
and 3 units up. _______________________
21.
____________________