Section 9.1 Day 2 Graphing Quadratic Functions Algebra 1 Section 9.1 Day 2 Graphing Quadratic Functions
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
Graphing Procedure 1. Create a table with 5 points 2. Find the vertex and plug those values into the middle of the table. 3. Choose two x-values on either side of the vertex and plug into the function to find the y-values 4. Graph the points 5. Check to make sure the graph is a parabola
Example 1: Graphing Graph 𝑓 𝑥 = 𝑥 2 +4𝑥+3 Vertex: 𝒙 𝒇(𝒙) −4 3 −3 −2 −1 𝒙 𝒇(𝒙) −4 −3 −2 −1 𝒙 𝒇(𝒙) Graph 𝑓 𝑥 = 𝑥 2 +4𝑥+3 Vertex: − 𝑏 2𝑎 =− 4 2 1 =−2 𝑓 −2 = −2 2 +4 −2 + 3=−1 (−2, −1) Plug values into 𝑓(𝑥) to find the coordinate pairs:
Example 1: Identifying Axis of Symmetry: Vertex: # of Zeros: 𝑥=−2 Vertex: (−2, −1) # of Zeros: 2 (x-intercepts) Maximum/Minimum: Minimum Domain: All Real Numbers Range: 𝑦≥−1
Example 2: Graphing 𝒙 𝒇(𝒙) −1 −5 1 2 − 1 2 1 2 𝒙 𝒇(𝒙) −1 1 2 1 2 𝒙 1 2 − 1 2 1 2 𝒙 𝒇(𝒙) −1 1 2 1 2 𝒙 𝒇(𝒙) Graph 𝑓 𝑥 =−2 𝑥 2 +2𝑥−1 Vertex: − 𝑏 2𝑎 =− 2 2 −2 = 1 2 𝑓 1 2 =−1 1 2 2 +2 1 2 −1= − 1 2
Example 2: Identifying Axis of Symmetry: Vertex: # of Zeros: 𝑥= 1 2 Vertex: ( 1 2 , − 1 2 ) # of Zeros: 0 (x-intercepts) Maximum/Minimum: Maximum Domain: All Real Numbers Range: 𝑦≤− 1 2
Example 3: Graphing 𝒙 𝒇(𝒙) −1 11 2 1 3 𝒙 𝒇(𝒙) −1 1 2 3 𝒙 𝒇(𝒙) 2 1 3 𝒙 𝒇(𝒙) −1 1 2 3 𝒙 𝒇(𝒙) Graph 𝑓 𝑥 =3 𝑥 2 −6𝑥+2 Vertex: − 𝑏 2𝑎 =− −6 2 3 =1 𝑓 1 =3 1 2 −6 1 +2=−1
Example 3: Identifying Axis of Symmetry: Vertex: # of Zeros: 𝑥=1 Vertex: (1, −1) # of Zeros: 2 (x-intercepts) Maximum/Minimum: Minimum Domain: All Real Numbers Range: 𝑦≥−1
Calculator Procedure Y= “enter in the quadratic equation” 2nd window/tblset Indpnt: Ask 2nd graph/table Enter in x-values To graph, click the graph button