Notes Over 5.7Graphing a Quadratic InequalityGraphing a Quadratic Inequality

2 .1 2 xy

2 a

b

Vertex:0

10

,0

2 2 y 02y

2

Normal Graph

Solid

Check (0,0)

20

Graph the inequality.

Notes Over 5.7Graphing a Quadratic InequalityGraphing a Quadratic Inequality

xxy 2 .2 2

2 a

b

Vertex:2

12

2

,1

2 2 y 1

1y

1

12

Down-Normal

1

Dotted

Check (1,0)

10

Graph the inequality.

1

Notes Over 5.7Graphing a Quadratic InequalityGraphing a Quadratic Inequality

22 .3 xy

2 a

b

Vertex:0

20

,0

2 2y 00y

0

2 times as fast

Solid

Check (0,1)

01

Graph the inequality.

Notes Over 5.7Graphing a System of Quadratic InequalitiesGraphing a System of Quadratic Inequalities

4

.42

2

xy

xy Vertex: ,0 0

Down/Normal

Solid

Check (0,-1)

01

Graph the system of inequalities.

Vertex: ,0 4

Up/Normal

Solid

Check (0, 0)

40

Notes Over 5.7Graphing a System of Quadratic InequalitiesGraphing a System of Quadratic Inequalities

2

2

4

.5

xxy

xy

Vertex: ,0 0

Up/Normal

Solid

Check (0,1)

01

Graph the system of inequalities.

Vertex: ,2 4

Down/Normal

Solid

Check (1, 0)

30

Notes Over 5.7Solving a Quadratic Inequality by Graphing Solving a Quadratic Inequality by Graphing

320 .6 2 xxSolid

Solve the inequality by graphing.

0 x2 x3 1

2

3 1

12

3 x

Where is the graph below 0?

1 3 1 3 20 xx

Notes Over 5.7Solving a Quadratic Inequality by Graphing Solving a Quadratic Inequality by Graphing

820 .7 2 xxSolid

Solve the inequality by graphing.

0 x x4 24 2

42 x

Where is the graph below 0?

0822 xx

Notes Over 5.7Solving a Quadratic Inequality by Graphing Solving a Quadratic Inequality by Graphing

20620 .8 2 xxDotted

Solve the inequality by graphing.

0 2 x x2 52 5

52 xWhere is the graph below 0?

0 2 2x x3 10

Notes Over 5.7Solving a Quadratic Inequality Algebraically Solving a Quadratic Inequality Algebraically

0103 .9 2 xxSolve the inequality algebraically.

0 x x2 52 5 These are critical values

l l l l l l l l l l l l l-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

Open Circles

What kind of value is inside each interval?

103332

1099

100302

100

10636

2 101836

52 x

01832 xx

Notes Over 5.7Solving a Quadratic Inequality Algebraically Solving a Quadratic Inequality Algebraically

183 .10 2 xxSolve the inequality algebraically.

0 x x6 36 3 These are critical values

l l l l l l l l l l l l l-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5

Closed Circles

What kind of value is inside each interval?

187372

182149

180302

180

18434

2 181216

3or 6 xx

01252 2 xx

Notes Over 5.7Solving a Quadratic Inequality Algebraically Solving a Quadratic Inequality Algebraically

1252 .11 2 xxSolve the inequality algebraically.

0 x2 x3 42/3 4 These are critical values

l l l l l l l l l l l l l-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5

Closed Circles

What kind of value is inside each interval?

1255522

122550

1205022

120

122522

2 12108

2/34 x

Notes Over 5.7