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Chapter 3 Quadratic Functions 3.1 Introduction to the Family of Quadratic Functions

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Key Points • The general formula for quadratic functions • Finding the zeros of a quadratic function
Finding the Zeros of a Quadratic Function Example Find the zeros of f ( x ) = 7 x 2 + 16 x + 4. Functions Modeling Change: A Preparation for Calculus, 4th

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Finding the Zeros of a Quadratic Function Example 3 The figure shows a graph of y = h ( x ) = − ½ x 2 − 2. What happens if we try to use algebra to find the zeros of h ? Since is not a real number, there are no real solutions, so h has no real zeros. This corresponds to the fact that the graph of h in the figure does not cross the x -axis. Functions Modeling Change: A Preparation for Calculus, 4th 3 2 1 1 2 3 x 5 4 3 2 1 y 4 -
Concavity and Quadratic Functions Example 3 Let f ( x ) = x 2 . Find the average rate of change of f over the intervals of length 2 starting at x = −4 and ending at x = 4. What do these rates tell you about the concavity of the

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