Intermediate Algebra (11th edition)

SECTION 9.1 The Square Root Property and Completing the Square 559

9.1

quadratic equation

9.2

quadratic formula
discriminant

9.3

quadratic in form

9.5

parabola

vertex

axis

quadratic function

9.7

quadratic inequality

rational inequality

KEY TERMS

SUMMARY

CHAPTER 9

1.The quadratic formulais
A.a formula to find the number of
solutions of a quadratic equation
B.a formula to find the type of
solutions of a quadratic equation
C.the standard form of a quadratic
equation
D.a general formula for solving any
quadratic equation.

2.A quadratic functionis a function
that can be written in the form
A. for real numbers
mand b
B. where
C. for real
numbers a, b, and c
D.ƒ 1 x 2 = 2 xfor xÚ0.

1 aZ 02

ƒ 1 x 2 =ax^2 +bx+c

ƒ 1 x 2 = Q 1 x 2 Z 0

P 1 x 2

Q 1 x 2 ,

ƒ 1 x 2 =mx+b

3.A parabolais the graph of

A.any equation in two variables

B.a linear equation

C.an equation of degree 3

D.a quadratic equation in two

variables, where one is first-

degree.

4.The vertexof a parabola is

A.the point where the graph

intersects the y-axis

B.the point where the graph

intersects the x-axis

C.the lowest point on a parabola

that opens up or the highest point

on a parabola that opens down

D.the origin.

5.The axisof a parabola is

A.either the x-axis or the y-axis

B.the vertical line (of a vertical

parabola) or the horizontal line

(of a horizontal parabola)

through the vertex

C.the lowest or highest point on the

graph of a parabola

D.a line through the origin.

6.A parabola is symmetric about its

axissince

A.its graph is near the axis

B.its graph is identical on each side

of the axis

C.its graph looks different on each

side of the axis

D.its graph intersects the axis.

TEST YOUR WORD POWER

See how well you have learned the vocabulary in this chapter.

ANSWERS

1.D; Example:The solutions of are given by 2.C; Examples:

3.D; Examples:See the figures in the Quick Review for Sections 9.5 and 9.6. 4.C; Example:
The graph of has vertex which is the lowest point on the graph. 5.B; Example:The axis of is the vertical line
x=-3. 6.B; Example:Since the graph of y= 1 x+ 322 is symmetric about its axis x=-3,the points 1 - 2, 1 2 and 1 - 4, 1 2 are on the graph.

y= 1 x+ 322 1 - 3, 0 2 , y= 1 x+ 322

ƒ 1 x 2 = 1 x+ 422 +1,ƒ 1 x 2 =x^2 - 4 x+ 5

x= ƒ 1 x 2 =x^2 - 2,

• b 2 b^2 - 4 ac
  2 a
  ax^2 +bx+c= 01 aZ 02.

9.1 The Square Root Property and

Completing the Square

Square Root Property

If xand kare complex numbers and then

x 2 k or x 2 k.

x^2 =k,

Solve

or

or

The solution set is E 1 + 222 , 1- 222 F,or E 1  222 F.

x= 1 + 222 x = 1 - 222

x- 1 = 28 x - 1 =- 28

1 x- 122 =8.

QUICK REVIEW

CONCEPTS EXAMPLES

CHAPTER 9 Summary 559

(continued)