1. Section 9.1 Day 2 Graphing Quadratic Functions
Algebra 1
Section 9.1 Day 2 Graphing Quadratic Functions

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. Graphing Procedure 1. Create a table with 5 points
2. Find the vertex and plug those values into the middle of the table.
3. Choose two x-values on either side of the vertex and plug into the function to find the y-values
4. Graph the points
5. Check to make sure the graph is a parabola

4. Example 1: Graphing Graph 𝑓 𝑥 = 𝑥 2 +4𝑥+3 Vertex:𝒙
𝒇(𝒙) −4 3 −3 −2 −1 𝒙
𝒇(𝒙) −4 −3 −2 −1 𝒙
𝒇(𝒙)
Graph 𝑓 𝑥 = 𝑥 2 +4𝑥+3
Vertex:
− 𝑏 2𝑎 =− =−2
𝑓 −2 = − −2 + 3=−1
(−2, −1)
Plug values into 𝑓(𝑥) to find the coordinate pairs:

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

6. Example 2: Graphing 𝒙 𝒇(𝒙) −1 −5 1 2 − 1 2 1 2 𝒙 𝒇(𝒙) −1 1 2 1 2 𝒙
1 2
− 1 2 1 2 𝒙
𝒇(𝒙) −1
1 2 1 2 𝒙
𝒇(𝒙)
Graph 𝑓 𝑥 =−2 𝑥 2 +2𝑥−1
Vertex:
− 𝑏 2𝑎 =− 2 2 −2 = 1 2
𝑓 =− −1= − 1 2

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

8. Example 3: Graphing 𝒙 𝒇(𝒙) −1 11 2 1 3 𝒙 𝒇(𝒙) −1 1 2 3 𝒙 𝒇(𝒙)2 1 3 𝒙
𝒇(𝒙) −1 1 2 3 𝒙
𝒇(𝒙)
Graph 𝑓 𝑥 =3 𝑥 2 −6𝑥+2
Vertex:
− 𝑏 2𝑎 =− − =1
𝑓 1 = −6 1 +2=−1

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

10. Calculator Procedure Y= “enter in the quadratic equation”
2nd window/tblset
Indpnt: Ask
2nd graph/table
Enter in x-values
To graph, click the graph button