5-7 Reteach

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Name. Date. Class. LESSON. 5-7. Graphing quadratic inequalities is similar to graphing linear inequalities. Graph y x 2. 2x. 3. Step 1 Draw the graph of y x 2. 2x.
Name LESSON

5-7

Date

Class

Reteach Solving Quadratic Inequalities

Graphing quadratic inequalities is similar to graphing linear inequalities. 2 Graph y  x  2x  3.

Step 1

2 Draw the graph of y  x  2x  3.



• a  1, so the parabola opens downward. • vertex at (1, 4) b  ______ 2  1, and f  1   4 ___ 2a 2  1  • y-intercept is 3, so the curve also passes through (2, 3)

      

   

Draw a solid boundary line for  or .

Step 3











X



(Draw a dashed boundary line for  or .) Step 2

Y



Shade below the boundary of the parabola for  or . (Shade above the boundary for  or .)

 

Check using a test point in the shaded region. Use  0, 0 . 2 y  x  2x  3 2 ?: 0    0   2  0   3

✓:03 Graph each inequality. 1. y  x 2  4x  3

2. y  x 2  4x 1

 2, 1 

Vertex:

3

y-intercept:

1

y-intercept:

solid boundary

Boundary:

 2, 3 

Vertex:

dashed boundary

Boundary:

Test point: (1, 1)

Test point: (1, 0)

10 

02

Y















       

Y

 









X

      

















Copyright © by Holt, Rinehart and Winston. All rights reserved.

a207c05-7_rt.indd 54

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X

Holt Algebra 2

12/15/05 4:37:04 PM Process Black

Name

Date

Class

Reteach

LESSON

5-7

Solving Quadratic Inequalities (continued)

You can use algebra to solve quadratic inequalities. 2 Solve the inequality x  2x  5  3.

Step 1

Write the related equation.

Step 2

Solve the equation.

2 x  2x  5  3

2 x  2x  8  0

Write the equation in standard form. Then factor to solve for x.

x

 4  x  2   0

x

 4   0 or  x  2   0

These solutions are called critical values.

x  4 or x  2 Step 3

Use the critical values to write three intervals. Intervals: x  2, 2  x  4, x  4

Step 4

Using the inequality, test a value for x in each interval. 2 x  2x  5  3 2 Try 3.  3   2  3   5  3?

x  2:

10  3 False. 2  x  4:

 0  2  2  0   5  3?

Try 0.

5  3 True. x  4:

 5  2  2  5   5  3?

Try 5.

10  3 False. Step 5

Use closed circles when the inequality is  or .

Shade the solution on a number line.     











Use open circles when the inequality is  or .



Solve each inequality. Graph the solution on the number line. 3. x  2x  1  4

4. x  x  4  6

2

2

3

Solve: x 2  2x 



0

.

Solve:

1, 3

Critical values:



Copyright © by Holt, Rinehart and Winston. All rights reserved.

a207c05-7_rt.indd 55









3, 0, 2

Test x-values:

x  1 or x  3     

2, 1

Critical values:

2, 0, 4

Test x-values:

x2  x  2  0

2  x  1 

    

55













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