Algebra Know-It-ALL

Part Three 513

The fact that d < 0 tells us that the function has no real zeros, just as it tells us that the qua-
dratic equation

− 3 x^2 + 7 x− 11 = 0

has no real roots.

Question 24-9

What are the coordinates (xv,yv) of the vertex point in the graph of the function stated in
Question 24-8? Is the vertex an absolute maximum or an absolute minimum?

Answer 24-9

Thex-coordinate of the vertex point, xv, can be found by the formula

xv=−b/2a

–6 –4 2 6

2

6

–2

–4

x

y

4

–8

–10

(–2,0) (4,0)

(1,–9)

Figure 30-1 Illustration for Answer 24-7. This is the

graph of y = x^2 − 2 x− 8.