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
54
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
Holt Algebra 2
12/15/05 4:37:07 PM Process Black
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