Unformatted text preview: −4 −3 −2 −1 3. f (x) = ||x| − 4|
5. (a) x = −1 or x = 9 2 (c) x = 0 or x = 2
(d) x = − 10 1 2 3 x 2.3 Quadratic Functions 2.3 139 Quadratic Functions You may recall studying quadratic equations in Intermediate Algebra. In this section, we review
those equations in the context of our next family of functions: the quadratic functions.
Definition 2.5. A quadratic function is a function of the form
f (x) = ax2 + bx + c,
where a, b, and c are real numbers with a = 0. The domain of a quadratic function is (−∞, ∞).
Example 2.3.1. Graph each of the following quadratic functions. Find the zeros of each function
and the x- and y -intercepts of each graph, if any exist. From the graph, determine the domain and
range of each function, list the intervals on which the function is increasing, decreasing, or constant
and ﬁnd the relative and absolute extrema, if they exist.
1. f (x) = x2 − 4x + 3. 2. g (x) = −2(x − 3)2 + 1. Solution.
1. To ﬁnd the zeros of f , we set f (x) = 0 and solve the equa...
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