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9-1 Graphing Quadratic Functions

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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 π‘Žβ‰ 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 π’™βˆ’π’—π’‚π’π’–π’†=βˆ’ 𝒃 πŸπ’‚ , π’šβˆ’π’—π’‚π’π’–π’†=π’‘π’π’–π’ˆ π’Šπ’ 𝒙. Step 2: Find the Axis of Symmetry 𝒙=βˆ’ 𝒃 πŸπ’‚ (π’™βˆ’π’—π’‚π’π’–π’† 𝒐𝒇 𝒗𝒆𝒓𝒕𝒆𝒙 Step 3: Find the π’š – π’Šπ’π’•π’†π’“π’„π’†π’‘π’• Plug in 0 for 𝒙 Step 4: Use symmetry to find additional points Plug in additional π’™βˆ’π’—π’‚π’π’–π’†π’” 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= βˆ’π‘₯ 2 +6π‘₯βˆ’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=π‘Ž π‘₯ 2 +𝑏π‘₯+𝑐 opens upward. The lowest point on the graph is the minimum. When 𝒂<𝟎, the graph of 𝑦=π‘Ž π‘₯ 2 +𝑏π‘₯+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 π‘₯ =2 π‘₯ 2 βˆ’4π‘₯βˆ’1 b. 𝑓 π‘₯ =βˆ’ π‘₯ 2 βˆ’2π‘₯βˆ’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 β„Ž π‘₯ =βˆ’16 π‘₯ 2 +48π‘₯+6, where β„Ž(π‘₯) represents the height in feet of the T-Shirt after π‘₯ 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


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