Section 9.1 Day 4 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

Intercept Form Intercept Form: 𝑦=𝑎(𝑥−𝑝)(𝑥−𝑞) Graphing Procedure: Identify the vertex: 𝑥= 𝑝+𝑞 2 Identify the Intercepts: 𝑝,0 , (𝑞,0) Plot the points Confirm the parabola shape

Example 1: Graphing 𝒙 𝒇(𝒙) 𝒙 𝒇(𝒙) 2 −4 −1 −9 Graph 𝑓 𝑥 =(𝑥−2)(𝑥+4) −4 −1 −9 Graph 𝑓 𝑥 =(𝑥−2)(𝑥+4) Intercepts: 2, 0 , −4,0 Vertex: (−1, −9)

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

Example 2: Graphing 𝒙 𝒇(𝒙) 3 −2 1 2 6 1 4 𝒙 𝒇(𝒙) Vertex: 1 2 ,6 1 4 Intercepts: 3, 0 , (−2,0) 𝒙 𝒇(𝒙) 3 −2 1 2 6 1 4 𝒙 𝒇(𝒙)

Example 2: Identifying Axis of Symmetry: Vertex: # of Zeros: 𝑥= 1 2 Vertex: ( 1 2 ,6 1 4 ) # of Zeros: 2 (x-intercepts) Maximum/Minimum: Maximum Domain: All Real Numbers Range: 𝑦≤6 1 4

Example 3: Graphing 𝒙 𝒇(𝒙) 𝒙 𝒇(𝒙) 1 −3 −1 −4 Graph 𝑓 𝑥 =(𝑥−1)(𝑥+3) −3 −1 −4 Graph 𝑓 𝑥 =(𝑥−1)(𝑥+3) Vertex: (−1, −4) Intercept: 1,0 , (−3,0)

Example 3: Identifying Axis of Symmetry: Vertex: # of Zeros: 𝑥=−1 Vertex: (−1,− 4) # of Zeros: 2 (x-intercepts) Maximum/Minimum: Minimum Domain: All Real Numbers Range: 𝑦≥−4