Beginning Algebra, 11th Edition

CHAPTER 9 Summary 587

EXERCISES 37 – 42

FOR INDIVIDUAL OR GROUP WORK

We can use a graphing calculator to illustrate how the graph of can be transformed

through arithmetic operations. Work Exercises 37– 42 in order.

37.In the standard viewing window of your calculator, graph the following one at a

time, leaving the previous graphs on the screen as you move along.

Describe the effect the successive coefficients have on the parabola.

38.Repeat Exercise 37for the following.

39.In the standard viewing window of your calculator, graph the following pair of

parabolas on the same screen.

Describe how the graph of can be obtained from the graph of.

40.In the standard viewing window of your calculator, graph the following parabolas

on the same screen.

Make a conjecture about what happens when the coefficient of is negative.

41.In the standard viewing window of your calculator, graph the following one at a

time, leaving the previous graphs on the screen as you move along.

Describe the effect that adding or subtracting a constant has on the parabola.

42.Repeat Exercise 41for the following.

Y 1 =x^2 Y 2 = 1 x+ 322 Y 3 = 1 x- 622

Y 1 =x^2 Y 2 =x^2 + 3 Y 3 =x^2 - 6

x^2

Y 1 =-x^2 Y 2 =- 2 x^2 Y 3 =- 3 x^2 Y 4 =- 4 x^2

Y 2 Y 1

Y 1 =x^2 Y 2 =-x^2

Y 4 =

1

8

Y 3 = x^2

1

4

Y 2 = x^2

1

2

Y 1 =x^2 x^2

Y 1 =x^2 Y 2 = 2 x^2 Y 3 = 3 x^2 Y 4 = 4 x^2

y=x^2

RELATING CONCEPTS

9.1

quadratic equation

9.2
completing the square

9.3

quadratic formula

discriminant

9.4

complex number

pure imaginary number

real part

imaginary part

standard form (of a complex

number)

conjugate (of a complex

number)

9.5

parabola

vertex

axis (of symmetry)

quadratic function

KEY TERMS

SUMMARY

CHAPTER 9