Intermediate Algebra (11th edition)

Graphing a Generalized Square Root Function
To graph a generalized square root function defined by

for an algebraic expression u, with square each
side so that the equation can be easily recognized. Then
graph only the part indicated by the original equation.

uÚ0,

ƒ 1 x 2  2 u

Graph

Square each side and rearrange terms to get

This equation has a circle as its graph.

However, graph only the lower half of the

circle, since the original equation indicates

thatycannot be positive.

x^2 +y^2 =4.

y=- 24 - x^2.

CONCEPTS EXAMPLES

x

y

2

–2

–2

0

y = –√4–x^2

11.4 Nonlinear Systems of Equations

Solving a Nonlinear System
A nonlinear system can be solved by the substitution
method, the elimination method, or a combination of the
two.

Solve the system.

(1)

(2)

Multiply equation (2) by and use elimination.

Solve for yto obtain and substitute into equation (2).

(2)

Let.

Apply the exponent.

Multiply by. Add

Factor.

or Zero-factor property

Find corresponding y-values to get the solution set

51 3, 5 2 , 1 - 3,- 52 , 15 i,- 3 i 2 , 1 - 5 i, 3i 26.

x= 3 x= 5 i

1 x^2 - 921 x^2 + 252 = 0

x^4 + 16 x^2 - 225 = 0 x^216 x^2.

x^2 -

225

x^2

=- 16

x^2 - a y=^15 x

15

x

b

2

=- 16

x^2 - y^2 =- 16

xy= 15 y=^15 x,

xy= 15

2 xy = 30

• x^2 +y^2 = 16

x^2 + 2 xy-y^2 = 14

- 1

x^2 - y^2 =- 16

x^2 + 2 xy-y^2 = 14

11.5 Second-Degree Inequalities and

Systems of Inequalities

Graphing a Second-Degree Inequality
To graph a second-degree inequality, graph the corre-
sponding equation as a boundary and use test points to
determine which region(s) form the solution set. Shade
the appropriate region(s).

Graphing a System of Inequalities
The solution set of a system of inequalities is the
intersection of the solution sets of the individual
inequalities.

Graph

yÚx^2 - 2 x+3.

0 x

y

1

(1, 2)

3

x

y

3

5

(^05)
Graph the solution set of the
system
x^2 +y^2 ...25.
3 x- 5 y7- 15

CHAPTER 11 Summary 671