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5.1 Transforming Quadratics

9.2.2.3 Sketch graphs of linear, quadratic and exponential functions, and translate between graphs, tables and symbolic representations. Know how to use graphing technology to graph these functions. 5.1 Transforming Quadratics.

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5.1 Transforming Quadratics

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  1. 9.2.2.3 Sketch graphs of linear, quadratic and exponential functions, and translate between graphs, tables and symbolic representations. Know how to use graphing technology to graph these functions. 5.1 Transforming Quadratics

  2. Guiding Question: How does the parent function of a graph get manipulated? • Lesson Objective: I will be able to transform the Quadratic Function & describe the changes of the quadratic function in vertex form. • Key Words: Quadratic Fcn., Parabola, Vertex, Vertex Form

  3. Guiding Question: How does the parent function of a graph get manipulated? • Parent Function • f(x) = x2 • This shape is called a parabola. • The origin (0,0) is where the graph starts and is called • the vertex.

  4. Guiding Question: How does the parent function of a graph get manipulated? • The Vertex Form of a quadratic function is • f(x) = a ( x – h)2 + k • It is called the vertex form because the vertex (starting pt) is at (h, k). • h = Horizontal shift - When his positive (x – h), the graph shifts right h units - When h is negative (x + h), the graph shifts left hunits. • k = Vertical shift - When k is positive, the graph shifts up - When k is negative, the graph shifts down VERTEX FORM

  5. Guiding Question: How does the parent function of a graph get manipulated? • a = shrink, stretch, reflection - If a is negative, the graph flips over - If a is a whole number, the graph shrinks - If a is a fraction, the graph widens • The Vertex Form of a quadratic function is • f(x) = a ( x – h)2 + k

  6. Guiding Question: How does the parent function of a graph get manipulated? • 1. y = (x + 1)2 – 2 • Graph this, how does it change

  7. Guiding Question: How does the parent function of a graph get manipulated? • How does this change the graph? • y = - (x – 1)2 - 3

  8. Guiding Question: How does the parent function of a graph get manipulated? • Assignment: TBD

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