1. Section 9.1 Day 2 Graphing Quadratic Functions
Algebra 1

2. Learning Targets
Define and identify a quadratic function in standard form
Identify a parabola shape and graph which is unique to the quadratic function
Define and identify the axis of symmetry, vertex, number of zeros, domain and range of a quadratic graph
Identify if the quadratic function has a graph with a maximum or a minimum
Graph a quadratic function using a table

3. Recall: Standard Form Standard Form: 𝑎 𝑥 2 +𝑏𝑥+𝑐 Graphing Procedure:
Find the vertex 𝑥=− 𝑏 2𝑎
Fill in a 5 point table with the vertex as the center
Plot the points
Confirm the parabola shape

4. Vertex Form Vertex Form: 𝑦=𝑎 𝑥−ℎ 2 +𝑘 Graphing Procedure:
Identify the vertex: (ℎ, 𝑘)
Fill in a 5 point table with the vertex as the center
Plot the points
Confirm the parabola shape

5. Example 1: Graphing 𝒙 𝒇(𝒙) 2 5 3 4 1 6 𝒙 𝒇(𝒙) Graph 𝑓 𝑥 = 𝑥−4 2 +1
Vertex: (4, 1) 𝒙
𝒇(𝒙) 2 5 3 4 1 6 𝒙
𝒇(𝒙)

6. Example 1: Identifying Axis of Symmetry: Vertex: # of Zeros:
𝑥=4
Vertex:
(4, 1)
# of Zeros:
0 (x-intercepts)
Maximum/Minimum:
Minimum
Domain:
All Real Numbers
Range:
𝑦≥1

7. Example 2: Graphing 𝒙 𝒇(𝒙) −3 −6 −2 −1 2 1 𝒙 𝒇(𝒙)
Vertex: (−1, 2) 𝒙
𝒇(𝒙) −3 −6 −2 −1 2 1 𝒙
𝒇(𝒙)

8. Example 2: Identifying Axis of Symmetry: Vertex: # of Zeros:
𝑥=−1
Vertex:
(−1, 2)
# of Zeros:
2 (x-intercepts)
Maximum/Minimum:
Maximum
Domain:
All Real Numbers
Range:
𝑦≤2

9. Example 3: Graphing 𝒙 𝒇(𝒙) 8 1 −1 2 −4 3 4 𝒙 𝒇(𝒙)
Vertex: (2, −4) 𝒙
𝒇(𝒙) 8 1 −1 2 −4 3 4 𝒙
𝒇(𝒙)

10. Example 3: Identifying Axis of Symmetry: Vertex: # of Zeros:
𝑥=2
Vertex:
(2,− 4)
# of Zeros:
2 (x-intercepts)
Maximum/Minimum:
Minimum
Domain:
All Real Numbers
Range:
𝑦≥−4

11. Intercept Form Intercept Form: 𝑦=𝑎(𝑥−𝑝)(𝑥−𝑞) Graphing Procedure:
Identify the vertex: 𝑥= 𝑝+𝑞 2
Identify the Intercepts: 𝑝,0 , (𝑞,0)
Plot the points
Confirm the parabola shape

12. Example 1: Graphing 𝒙 𝒇(𝒙) 2 −4 −1 −9 𝒙 𝒇(𝒙) Graph 𝑓 𝑥 =(𝑥−2)(𝑥+4)
Intercepts: 2, 0 , −4,0
Vertex: (−1, −9) 𝒙
𝒇(𝒙) 2 −4 −1 −9 𝒙
𝒇(𝒙)

13. Example 1: Identifying Axis of Symmetry: Vertex: # of Zeros:
𝑥=−1
Vertex:
(−1,−9)
# of Zeros:
2 (x-intercepts)
Maximum/Minimum:
Minimum
Domain:
All Real Numbers
Range:
𝑦≥−9

14. Example 2: Graphing 𝒙 𝒇(𝒙) 3 −2 1 2 6 1 4 𝒙 𝒇(𝒙)
Vertex: ,6 1 4
Intercepts: 3, 0 , (−2,0) 𝒙
𝒇(𝒙) 3 −2
1 2
6 1 4 𝒙
𝒇(𝒙)

15. Example 2: Identifying Axis of Symmetry: Vertex: # of Zeros:
𝑥= 1 2
Vertex:
( 1 2 ,6 1 4 )
# of Zeros:
2 (x-intercepts)
Maximum/Minimum:
Maximum
Domain:
All Real Numbers
Range:
𝑦≤6 1 4

16. Example 3: Graphing 𝒙 𝒇(𝒙) 1 −3 −1 −4 𝒙 𝒇(𝒙) Graph 𝑓 𝑥 =(𝑥−1)(𝑥+3)
Vertex: (−1, −4)
Intercept: 1,0 , (−3,0) 𝒙
𝒇(𝒙) 1 −3 −1 −4 𝒙
𝒇(𝒙)

17. Example 3: Identifying Axis of Symmetry: Vertex: # of Zeros:
𝑥=−1
Vertex:
(−1,− 4)
# of Zeros:
2 (x-intercepts)
Maximum/Minimum:
Minimum
Domain:
All Real Numbers
Range:
𝑦≥−4