1. Quadratic
Inequalities
5.7
Algebra 2

2. Graphing Inequalities
Draw the parabola and
shade the area indicated by
the inequality.

3. Graphing Inequalities
y > x2
- 2x -3
Use a
graphing calculator
to draw the
parabola.
(http://www.coolmath.com/graphit/)

4. Graphing Inequalities
y > x2
- 2x -3
Or use your notes
from 5.1 :)
Find the vertex and
the axis of
symmetry

5. Systems of Quadratic
Inequalities
Graph both parabolas first
using a graphing calculator.

6. Systems of Quadratic
Inequalities
Graph both parabolas first.
Then shade the areas
indicated.

7. Systems of Quadratic
Inequalities
Graph both parabolas first.
Then shade the areas
indicated.
The solution to the system
is the part that is shaded by
all inequalities. (If there are
no overlapping spots, there
is no solution.)

8. Solving Inequalities
Solve the equation to find
the “critical x-values.”

9. x2
+ 2x ≤ 8 ⇒ x2
+ 2x - 8 ≤ 0
Solve for 0.

10. x2
+ 2x ≤ 8 ⇒ x2
+ 2x - 8 ≤ 0
(x - 2)(x + 4) ≤ 0
Factor.

11. x2
+ 2x ≤ 8 ⇒ x2
+ 2x - 8 ≤ 0
(x - 2)(x + 4) ≤ 0
x - 2 = 0 and x + 4 = 0
Solve for x.
x = 2 and x = -4.

12. Solving Inequalities
Solve the equation to find
the “critical x-values.”
Plot the critical numbers on
a number line.
0-4 2

13. Solving Inequalities
Solve the equation to find
the “critical x-values.”
Plot the critical numbers on
a number line.
Notice that this breaks the
number line up into 3
sections.

14. Solving Inequalities
Solve the equation to find
the “critical x-values.”
Plot the critical numbers on
a number line.
Test a number inside each
region.
0-4 2

15. [-4, 2] is the solution.
Use square brackets if “less
than or equal to.” Use
parentheses if just “less
than” or “greater than.”