Beginning Algebra, 11th Edition

Solve each quadratic equation for complex solutions by the square root property, with.

Write solutions in standard form. See Example 5.

Solve each quadratic equation for complex solutions by the quadratic formula. Write solutions

in standard form. See Example 6.

Concept Check Answer trueorfalseto each statement. If false, say why.

61.Every real number is a complex number.

62.Every pure imaginary number is a complex number.

63.Every complex number is a real number.

64.Every complex number is a pure imaginary number.

Graph each linear equation. See Section 3.2.

Evaluate each expression for See Section 1.3.

67. 2 x^2 - x+ 1 68. 1 x- 122

x=3.

2 x- 3 y= 6 y= 4 x- 3

PREVIEW EXERCISES

4 x^2 + 3 =- 2 x x^2 - x+ 3 = 0 4 q^2 - 2 q+ 3 = 0

5 x^2 + 3 = 2 x 6 x^2 + 1 =- 2 x 2 m^2 + 7 =- 2 m

3 x^2 - 2 x+ 3 = 0 p^2 - 3 p+ 4 = 0 2 x^2 +x+ 3 = 0

m^2 - 2 m+ 2 = 0 x^2 - 4 x+ 5 = 0 2 r^2 + 3 r+ 5 = 0

1 x+ 622 =- 7 13 x+ 222 =- 18 14 x+ 122 =- 48

1 x+ 122 =- 4 1 x- 522 =- 36 1 x- 322 =- 5

k 60

13 - 14 i

12 + 24 i

• 5 + 10 i
  6 + 12 i

21 +i

4 +i

17 +i

5 + 2 i

• 4 + 2 i
  1 +i

7 + 3 i

1 - i

580 CHAPTER 9 Quadratic Equations

OBJECTIVES In Section 5.4,we graphed the quadratic equation By plotting points, we

obtained the graph of a parabola,shown here in FIGURE 2.

y=x^2.

More on Graphing Quadratic Equations;

Quadratic Functions

9.5

1 Graph quadratic

equations of

the form

2 Use a graph to

determine the

number of real

solutions of a

quadratic equation.

1 aZ 02.

y=ax^2 +bx+c

FIGURE 2

xy

39

24

11

00

1

4

• 3 9


• 2


• 1
  x

y

y = x^2

Axis

Vertex

–2 0 2

1

4

9

Recall that the lowest point on

this graph is called the vertexof the

parabola. (If the parabola opens down-

ward, the vertex is the highest point.)

The vertical line through the vertex is

called the axis,or axis of symmetry.

The two halves of the parabola are

mirror images of each other across

this axis.

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