1. Section 9.1 Day 3 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) 𝒙 𝒇(𝒙) −3 −6 −2 −1 2 1−1 2 1
Graph 𝑓 𝑥 =−2 𝑥
Vertex: (−1, 2)

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 −5 2 −4 3 4 𝒙 𝒇(𝒙)−8 1 −5 2 −4 3 4 𝒙
𝒇(𝒙)
Graph 𝑓 𝑥 =− 𝑥−2 2 −4
Vertex: (2, −4)

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