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2 Functions > 2.4 Quadratic Functions
2.4 Quadratic Functions
Introduction The squaring function y = x2 that played an important role in Section 2.2 is a member of a family of functions called quadratic functions.
DEFINITION 2.4.1 Quadratic Function
A quadratic function y = f (x) is a function of the form
where a ? 0, b, and c are constants.
The domain of a quadratic function f is the set of real numbers (-8, 8).
Graphs The graph of any quadratic function is called a parabola. The graph of a quadratic function has the same basic shape of the squaring function y = x2 shown in FIGURE 2.4.1. In the examples that follow we will see that the graphs of quadratic functions (1) are simply transformations of the graph of y = x2:
• The graph of f (x) = ax2, a > 0, is the graph of y = x2 stretched vertically when a 1, and compressed vertically when 0 < a < 1.
