1. 9-1 Graphing Quadratic Functions
I can:
find the vertex of a parabola.
find the axis of symmetry of a parabola
find the y-intercept of a quadratic
find the domain and range of a quadrat
graph a quadratic using its characteristics
9-1 Graphing Quadratic Functions

2. Quadratic Function
A quadratic function can be written in the standard form 𝒂 𝒙 𝟐 +𝒃𝒙+𝒄 where 𝑎≠0.
The shape of the graph of a quadratic is called a parabola.
Parabolas are symmetric about a central line called the axis of symmetry.
The axis of symmetry intersects a parabola at only one point, called the vertex.

3. To Graph a Quadratic: Step 5: Connect the points with a smooth curve
Step 1: Find the VERTEX
𝒙−𝒗𝒂𝒍𝒖𝒆=− 𝒃 𝟐𝒂 , 𝒚−𝒗𝒂𝒍𝒖𝒆=𝒑𝒍𝒖𝒈 𝒊𝒏 𝒙.
Step 2: Find the Axis of Symmetry
𝒙=− 𝒃 𝟐𝒂 (𝒙−𝒗𝒂𝒍𝒖𝒆 𝒐𝒇 𝒗𝒆𝒓𝒕𝒆𝒙
Step 3: Find the 𝒚 – 𝒊𝒏𝒕𝒆𝒓𝒄𝒆𝒑𝒕
Plug in 0 for 𝒙
Step 4: Use symmetry to find additional points
Plug in additional 𝒙−𝒗𝒂𝒍𝒖𝒆𝒔 around vertex
Step 5: Connect the points with a smooth curve

4. Example 1: Graph each Quadratic equation and state the domain and range.

5. Example 1: Graph each Quadratic equation and state the domain and range.
b. 𝑦= −𝑥 2 +6𝑥−2

6. Example 1: Graph each Quadratic equation and state the domain and range.

7. Example 2: Identify the vertex, axis of symmetry, and the y-intercept of each graph.
a b.

8. Maximum and Minimum Values:
When 𝒂>𝟎, the graph of 𝑦=𝑎 𝑥 2 +𝑏𝑥+𝑐 opens upward.
The lowest point on the graph is the minimum.
When 𝒂<𝟎, the graph of 𝑦=𝑎 𝑥 2 +𝑏𝑥+𝑐 opens downward.
The highest point on the graph is the maximum.

9. Example 3: Determine whether the function has a minimum or maximum value and then state the value.
a. 𝑓 𝑥 =2 𝑥 2 −4𝑥−1 b. 𝑓 𝑥 =− 𝑥 2 −2𝑥−2

10. At what height was the T-Shirt launched?
Example 4: The cheerleaders at Lake high School launch T-shirts into the crowd every time the Lakers score a touchdown. The height of the T-shirt can be modeled by the function ℎ 𝑥 =−16 𝑥 2 +48𝑥+6, where ℎ(𝑥) represents the height in feet of the T-Shirt after 𝑥 seconds.
Graph the function:
At what height was the T-Shirt launched?
What is the maximum height?
When was the maximum height reached?

11. Homework
9.1 Pages : 5 – 12, 17 – 20, 45, 46, 63