Section 9.1 Day 3 Graphing Quadratic Functions Algebra 1

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

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

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

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)

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

Example 2: Graphing 𝒙 𝒇(𝒙) 𝒙 𝒇(𝒙) −3 −6 −2 −1 2 1 −1 2 1 Graph 𝑓 𝑥 =−2 𝑥+1 2 +2 Vertex: (−1, 2)

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

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)

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