Graph the following quadratic functions and identify the vertex and axis of each:

(a) f(x) = x2 – 2 First select some representative values of x and solve for f(x). Then, using y for f(x), plot the resulting ordered pairs and connect them with a smooth line. The closer the points, the more accurate the graph. See Fig. 3-7.

(b) f(x) = −x2 + 4x + 32

Notice the symmetry about the axis: x = 2. For x = 2 ± 2, y = 32; for x = 2 ± 4, y = 20; for x = 2 ± 6, y = 0.

(c) f(x) = x2 – 8x + 17

Notice the symmetry about the axis: x = 4. For x = 4 ± 1, y = 2; for x = 4 ± 2, y = 5.

(d) f(x) = –x2 + 4x + 9

Transcribed Image Text:

X f(x) = x - 2 = y -3 f(-3)= (-3) - -2 f(-2)=(-2) - 2 -1 0 f(0) f(-1)=(-1) - 2 = (0)2 - 1 f(1) = (1) - 2 f(2) == (2)2 222222 I I = 7 = 2 = 3 f(3) = (3) - 2 = 2 - 2 = -1 = 2 = 7 Vertex: (0, -2). Axis: x = 0, which is the y axis_