1. Quadratic Inequalities
Lesson 3.3

2. Definition Recall the quadratic equation ax2 + bx + c = 0
Replace = sign with <, >, ≤, or ≥ makes it a quadratic inequality
Solving:
Find where the equality occurs
These values are the boundary numbers

3. Graphical Solutions
Graph of the quadratic y = ax2 + bx + c is a parabola
Extends upward or downward
Solution to y > 0 includes all x-values where graph is above the axis
Solution to y < 0 includes x-values where graph is below the axis

4. Try It Out Given Place in Y= screen, graph
Determine boundary values (zeros of equation)
Which values of x satisfy the inequality?

5. Another Version Consider 2x2 > 16
Create a graph of both sides of the inequality
Determine values of x which satisfy the equation, then the inequality or

6. Steps for Symbolic Solution
Write as an equation ax2 + bx + c = 0
Solve resulting equation for boundary numbers
Use boundary numbers to separate number line into disjoint intervals
Make a table of test values
One value from each interval
Use this to specify which intervals satisfy the original inequality

7. Example Try x2 – 9 < 0 Solve x2 – 9 = 0 • x = +3 or x = -3 x -5 -27 y 16 40
This is the interval

8. Using the Calculator Table
Place function in the Y= screen
Go to Table, ♦Y
Adjust start, increment as needed, F2
View intervals where results are
negative,
zero,
or positive
x2 – 9 < 0

9. Assignment
Lesson 3.3
Page 195
Exercises 1 – 39 odd