Graphing Quadratic Functions Worksheet
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1
2Algebra 2
Graphing Quadratic Functions
STANDARD FORM – Sketch the graph of each function using the vertex, the y-intercept, and
the y-intercept’s mirror point. Then state the maximum or minimum value of ��, and the
equation of the axis of symmetry.
2
1
1. �� = ��
− 8�� + 18
2
4. �� = −
��
− 10�� − 20
2
2
2. �� = 3��
+ 30�� + 100
2
5. �� = 4��
− 4�� + 1
2
3. �� = −2��
+ 4�� + 3
2
6. �� = −��
+ 10�� − 10
VERTEX FORM – Sketch the graph of each function using the vertex, the y-intercept, and the y-
intercept’s mirror point. Then state the maximum or minimum value of ��, and the equation of
the axis of symmetry.
2
2
7. �� = ( �� + 3 )
+ 4
10. �� = 4��
− 6
1
2
11. �� = −5 ( �� − 8 )
+ 220
2
( �� − 2 )
8. �� =
− 3
2
2
12. �� = 2 ( �� − 3 )
2
9. �� = −2 ( �� − 5 )
+ 10
INTERCEPT FORM – Sketch the graph of each function using the vertex and the x-intercepts.
Then state the maximum or minimum value of ��, and the equation of the axis of symmetry.
1
13. �� = ( �� − 3 )( �� − 9 )
16. �� =
(�� − 2)(�� − 10)
2
14. �� = 2(�� + 1)(�� − 7)
17. �� = −(�� + 3)(�� + 4)
15. �� = −3 ( �� + 2 )( �� − 4 )
18. �� = 4(�� + 2)(�� − 3)
Rewrite in standard form.
Rewrite in intercept form.
Rewrite in vertex form.
2
2
19. �� = −8 ( �� + 3 )( �� + 7 )
24. �� = ��
+ 14�� + 40
29. �� = ��
+ 8�� + 11
1
( �� + 6 )( �� − 2 )
2
2
20. �� =
25. �� = −5��
− 35�� + 90
30. �� = ��
− 2�� + 6
2
2
21. �� = 6 ( �� + 4 )
− 11
2
2
26. �� = 3��
− 48
31. �� = ��
− 14�� − 10
2
22. �� = 3 ( �� − 1 )
+ 5
2
2
27. �� = 2��
− �� − 15
32. �� = ��
+ 20�� + 108
2
2
( �� + 10 )
23. �� = −
− 16
2
2
28. �� = 4��
+ 23�� + 15
33. �� = ��
− 6�� − 1
5
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