Beginning Algebra, 11th Edition

588 CHAPTER 9 Quadratic Equations

positive or negative

( plus or minus)

 i imaginary unit

NEW SYMBOLS

1.Aquadratic equationis an
equation that can be written in the
form
A.
B.
C.
D.

2.Acomplex numberis
A.a real number that includes a
complex fraction
B.a nonzero multiple of i
C.a number of the form
where aandbare real numbers
D.the square root of -1.

a+bi,

y=mx+b.

Ax+B= 0

ax^2 +bx+c= 0

Ax+By=C

3.Apure imaginary numberis

A.a complex number where

B.a number that does not exist

C.a complex number where

D.any real number.

4.Aparabolais the graph of

A.any equation in two variables

B.a linear equation

C.an equation of degree three

D.a quadratic equation in two

variables.

b= 0

a+bi,

a=0,bZ 0

a+bi,

5.Thevertexof 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.

6.Theaxisof a vertical parabola is

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

B.the vertical line through the vertex

C.the horizontal line through the vertex

D.thex-axis.

TEST YOUR WORD POWER

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

ANSWERS

1.B;Examples: 2.C;Examples: , 7i ,
3.A;Examples: 4.D;Examples:SeeFIGURES 2–7inSection 9.5. 5.C;Example:The graph of has vertex
1 - 3, 0 2 ,which is the lowest point on the graph. 6.B;Example:The axis of the graph of y= 1 x+ 322 is the line x=-3.

2 i,- 13 i,i 26 y= 1 x+ 322

z^2 + 6 z+ 9 =0,y^2 - 2 y=8, 1 x+ 321 x- 12 = 5 - 51 or- 5 + 0 i 2 1 or 0+ 7 i 222 - 4 i

9.1 Solving Quadratic Equations by the

Square Root Property

Square Root Property
Ifkis positive and if then

or

The solution set, E- 2 k, 2 kF,can be written E 2 kF.

x 2 k x 2 k.

x^2 =k,

Solve

or

or

or

The solution set is e

• 1  25
  2

f.

x=

• 1 - 25
  2

x=

• 1 + 25
  2

2 x=- 1 + 25 2 x=- 1 - 25

2 x+ 1 = 25 2 x+ 1 =- 25

12 x+ 122 =5.

QUICK REVIEW

CONCEPTS EXAMPLES

9.2 Solving Quadratic Equations by

Completing the Square

Solving a Quadratic Equation by Completing the
Square

Step 1 If the coefficient of the second-degree term is
1, go to Step 2. If it is not 1, divide each side of
the equation by this coefficient.

Step 2 Make sure that all variable terms are on one
side of the equation and all constant terms are
on the other.

Solve

Divide by 2.

x^2 + 2 x= Add.^12

1

2

x^2 + 2 x-

1

2

= 0

2 x^2 + 4 x- 1 =0.

(continued)

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