7.4 The Graph of the Quadratic Function

  • The Parabola • Vertex and y-intercept • Solving Quadratic Equations Graphically

In this section, we discuss the graph of the quadratic function ax2 + bx + c and show the graphical solution of a quadratic equation. By letting y = ax2 + bx + c ,  we can graph this function, as in Chapter 3.

EXAMPLE 1 Graphing a quadratic function

Graph the function f(x) = x2 + 2x − 3.

First, let y = x2 + 2x − 3. Then set up a table of values and graph the function as shown in Fig. 7.11. We can also display it on a calculator as shown in Fig. 7.12.

A parabola opens upward, falls through (negative 4, 5), (negative 3, 0), and (negative 2, negative 3) to vertex (negative 1, negative 4), then rises through (0, negative 3), (1, 0), and (2, 5).

Fig. 7.11

Fig. 7.12

The shape of the graph in Figs. 7.11 and ...

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