1. Section 9.1 Day 1 Graphing Quadratic Functions
Algebra 1
Section 9.1 Day 1 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. Quadratic Function
Standard Form: 𝑎 𝑥 2 +𝑏𝑥+𝑐
Example: 2 𝑥 2 +4𝑥−1

4. Graph of a Quadratic Function
Parabola: The shape of a quadratic function (symmetric)
Continuous: All points are connected and the graph extends infinitely
Smooth Curve: There are no sharp turns or jagged edges
Non-Linear: Not a straight line

5. Axis of Symmetry & Vertex
Axis of Symmetry: The vertical line that divides the parabola graph into two symmetrical pieces
𝑥=− 𝑏 2𝑎
Vertex: The lowest or highest point on the parabola graph. This point intersects once with the Axis of Symmetry.

6. Axis of Symmetry & Vertex
𝑥=− 𝑏 2𝑎 =− = −1
𝒙=−𝟏
Vertex:
(−1, −3)

7. Number of Zeros Produced
The zeros of a function are synonymous with the x- intercepts of a function.
A parabola could have one zero, two zeros, or no zeros.

8. Maximum vs. Minimum
Some parabolas will open up and others will open down.
Parabolas that open up have a minimum which is the lowest point on the graph.
Parabolas that open down have a maximum which is the highest point on the graph.

9. Domain & Range
Domain: All the possible “x-values” that will satisfy a function.
Domain is all real numbers
Range: All the possible “y-values” produced by the function.
Range is 𝑦≥−3

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

11. Example 2: Identifying from a Graph
Axis of Symmetry:
𝑥=2
Vertex:
(2,5)
# of Zeros:
2 (x-intercepts)
Maximum/Minimum:
Maximum
Domain:
All Real Numbers
Range:
𝑦≤5

12. Example 3: Identifying from a Graph
Axis of Symmetry:
𝑥=−3
Vertex:
(−3, −5)
# of Zeros:
2 (x-intercepts)
Maximum/Minimum:
Minimum
Domain:
All Real Numbers
Range:
𝑦≥−5

13. Example 4: Identifying from a Graph
Axis of Symmetry:
𝑥=1
Vertex:
(1, −2)
# of Zeros:
0 (x-intercepts)
Maximum/Minimum:
Maximum
Domain:
All Real Numbers
Range:
𝑦≤−2