Quadratic Functions Unit Objectives: Solve a quadratic equation. Graph/Transform quadratic functions with/without a calculator Identify function attributes:

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Presentation transcript:

Quadratic Functions Unit Objectives: Solve a quadratic equation. Graph/Transform quadratic functions with/without a calculator Identify function attributes: domain, range, vertex, line of symmetry, number and nature of roots, maximum/minimum values. Model situations with quadratic functions. Today’s Objective: Identify attributes and graph quadratic functions

Parent function/equation: Quadratic Function: Graph: Parabola Axis of Symmetry (line) Divides the graph into 2 mirror images x = h

Translation: Vertical Translation: Horizontal Dilation: Reflection Up k units Down k units Right h units Left h units Stretch: Compression: Across x-axis

Graphing a Quadratic Function in vertex form 1.Plot the vertex 2.Find and plot two points to the right of vertex. 3.Plot the point across axis of symmetry. 4.Sketch the curve. Vertex: Axis of Symmetry: Domain: Range: All Real Numbers Units right of vertex x Units up from vertex 1 2

Graphing a Quadratic Function in vertex form 1.Plot the vertex 2.Find and plot two points to the right of vertex. 3.Plot the point across axis of symmetry. 4.Sketch the curve. Vertex: Axis of Symmetry: Domain: Range: All Real Numbers Units right of vertex x Units up from vertex 1 2

Graphing a Quadratic Function in vertex form 1.Plot the vertex 2.Find and plot two points to the right of vertex. 3.Plot the point across axis of symmetry. 4.Sketch the curve. Vertex: Axis of Symmetry: Domain: Range: All Real Numbers Units right of vertex x Units up from vertex 1 2

Identify the Vertex: Finding dilation factor: Choose another known point and solve for a. (-2, -7) (-1, -5)

Identify the Vertex: Finding dilation factor: Choose another known point and solve for a. (3, 9) (5, 7) Pg. 199 #7-37 odds