Use the three steps outlined in Section 3.6 for graphing y = ax2 + bx +

c, to sketch the following quadratic functions:

(a) y = −x2 + 10x – 16

(b) y = x2 – 8x + 18 (1) With a = 1 > 0, the parabola opens upward.

(3) With the vertex at (4, 2) and the parabola opening upward, there are no x intercepts. See Fig. 3-14.

(c) y = −2x2 + 10x – 8 (1) With a = −2

(3) −2x2 + 10x – 8 = 0 Dividing by −2, then factoring,

The coordinates of the x intercepts are (1, 0) and (4, 0). See Fig. 3-15.

To see how graphing similar functions can also be simplified by the process of completing the square, see Dowling, Schaum’s Outline of Calculus for Business, Economics, and the Social Sciences, Problem 3.25.

Transcribed Image Text:

(1) Here a = -1, b = 10, and c = 16. With a < 0, the parabola opens down. (2) -b x = = 2a -(10) 2(-1) 4ac-b 4(-1)(-16) (10) y = == 4a 4(-1) 64-100 -36 x = 5 y = = 9 -4 -4 The coordinates of the vertex are (5, 9). (3) Setting the equation equal to zero in preparation to find the x coordinates of the horizontal intercepts, -x+10x-16 = 0