Algebra Know-It-ALL

Part Three 515

Armed with this information, we can sketch the graph. To fit it into a neat space, let’s
use rectangular coordinates where each horizontal division is 1/4 unit and each vertical
division is 2 units, with the origin all the way up at the top. We can use a calculator as
a “point-plotting aid” and approximate the vertex (7/6, −83/12) as (1.17, −6.92). The
result is shown in Fig. 30-2.

Chapter 25

Question 25-1

What is the polynomial standard form of a cubic equation in the variable x?

Answer 25-1

When a cubic equation is in polynomial standard form and the variable is x, the equation can
be written like this:

ax^3 +bx^2 +cx+d= 0

where a,b,c, and d are real numbers, and a≠ 0.

Question 25-2

What is the binomial-cubed form of a cubic equation in the variable x?

x

y

12

–4

–8

(0,–11)

–16 (7/6,–83/12)

(2,–9)

Figure 30-2 Illustration for Answer 24-10. This is the

graph of y = − 3 x^2 + 7x− 11. On the x axis,

each increment is 1/4 unit. On the y axis,

each increment is 2 units.