4.3 Quadratic Functions and Their Properties PDF

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4.3 Quadratic Functions and Their Properties...

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4.3 Quadratic Functions and Their Properties Quadratic Function:

Use the Vertex, Axis of Symmetry, and Intercepts to Graph a Quadratic Function.

Example 1: Locate the vertex and axis of symmetry of the parabola defined by

Example 2: For the quadratic , answer the following. a) Does the graph open up or down? b) What are the coordinates of the vertex? c) What is the equation of the axis of symmetry? d) What is/are the x-intercept(s)? e) What is the y-intercept? f) Graph the function. g) Determine the domain and range of the function. h) Determine where the function is increasing and decreasing.

Does it open up or down?

Find a Quadratic Function Given Its Vertex and a Point.

1. Plug in vertex as h and k (h, k) and plug in the given point x and y (x, y) to obtain a. 2. Plug a and the vertex in, then simplify.

Example 3: Determine the quadratic function whose vertex is (1, -5) and whose y-intercept is -3.

Example 4: Find the minimum or maximum of the given quadratic.

Example 5 Determine the quadratic function whose vertex is (-2, -16) and whose x-intercepts is 2.

*show MML graphing example Example 6 The marginal cost of a product can be thought of as the cost of producing one additional unit of output. For example, if the marginal cost of producing the 50th product is $6.20, it cost $6.20 to increase production from 49 to 50 units of output. Suppose the marginal cost C (in dollars) to produce x thousand mp players is given by the function a) How many players should be produced to minimize the marginal cost? b) What is the minimum marginal cost?...