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Quadratic Functions

Quadratic Functions. Objectives: Graph a Quadratic Function using Transformations Identify the Vertex and Axis of Symmetry of a Quadratic Function Graph a Quadratic Function using its Vertex, Axis and Intercepts. Quadratic Function.

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Quadratic Functions

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  1. QuadraticFunctions Objectives: Graph a Quadratic Function using Transformations Identify the Vertex and Axis of Symmetry of a Quadratic Function Graph a Quadratic Function using its Vertex, Axis and Intercepts

  2. Quadratic Function • A function that is defined by a 2nd degree polynomial in one variable. The domain is • Standard form shows the vertex, the axis of symmetry and whether it opens up or down.

  3. Graphing Quadratic Function with Equations in Standard form • 1. Determine whether the parabola opens upward or downward • 2. Determine the vertex of the parabola • 3. Find the x-intercepts by solving • 4. Find the y-intercept by computing • 5. Plot the intercepts, the vertex, and additional points as necessary. Connect these points with a smooth curve that is shaped like a cup.

  4. Graph the quadratic function • 1. • 2.

  5. Graphing Quadratic Function with Equations in the form • 1. Determine whether the parabola opens upward or downward • 2. Determine the vertex of the parabola • 3. Find the axis of symmetry • 4. Find the y-intercept and the x-intercepts • 5. Plot the vertex, the axis of symmetry, y-intercept and its symmetry point. Connect these points with a smooth curve that is shaped like a cup.

  6. Graph each quadratic function by determining whether its graph opens up or down and by finding its vertex, axis of symmetry, y-intercept, and x-intercepts (if any). Determine the domain and the range of the function. Determine where the function is increasing and decreasing. • 3.

  7. Graph each quadratic function by determining whether its graph opens up or down and by finding its vertex, axis of symmetry, y-intercept, and x-intercepts (if any). Determine the domain and the range of the function. Determine where the function is increasing and decreasing. • 4.

  8. Determine the quadratic function whose graph is given. • 5.

  9. Minimum and Maximum of Quadratic Functions • If , then has a minimum that occurs at . This minimum value is • If , then has a maximum that occurs at . The maximum value is • 6. Determine, without graphing, whether the given quadratic function has a max or min value and find it

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