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3.3 Quadratic Functions

3.3 Quadratic Functions. Objectives: Define three forms for quadratic functions Find the vertex and intercepts of a quadratic function and sketch its graph Convert one form of a quadratic function to another. Quadratic Function: Graph Makes A Parabola Shape.

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3.3 Quadratic Functions

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  1. 3.3 Quadratic Functions Objectives: Define three forms for quadratic functions Find the vertex and intercepts of a quadratic function and sketch its graph Convert one form of a quadratic function to another

  2. Quadratic Function: Graph Makes A Parabola Shape • The rule of a quadratic function is a polynomial of degree 2. • The rule? Polynomial of degree 2? • Example:   What can we say about parabola?

  3. Three Forms of Writing a Quadratic Function • Transformation form: • Polynomial form: • x-Intercept form: Transformation Form *Most useful form for finding the vertex • Vertex: (h,k) • But how do we find the x and y intercepts? • (x,0) • (0,y) Be careful

  4. Example 1:Transformation Form

  5. Polynomial Form * Most useful for finding the y-intercept • y-intercept: • x-intercept: • Vertex: (think of the transformation form) Example 2: Polynomial Form

  6. X-intercept Form  Has to be in this Form * Most useful for finding the x-intercepts • x-intercept: • y-intercept: • Vertex: Example 3: X-intercept Form

  7. Summary and Changing from One Form to Another • Changing to a polynomial: Expand • Changing to a x-intercept: Expand and factor or use quadratic formula • Changing to a transformation: Expand and complete the square

  8. Applications Involving Finding Vertex Example 6: Maximum Area for a Fixed Perimeter 3.3 Hmwr: p. 171: Qu:1,7,10,15-45oddccccc, 51

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