Download 3.9 Graph & Solve Quadratic Inequalities

3.9 Warm Up
Solve using the quadratic
formula.
1. 2x² - 5x – 2 = 0
2. -6x² + 3x + 2 = 3
3. x² + 2x = 4
3.9 Graph & Solve
Quadratic Inequalities
Example 1 – Graph a system of
quadratic inequalities
• Graph the system
• y < -x² - x + 2
• y ≥ x² - 2x – 2
Step 1: Graph y < -x² - x + 2. Vertex & tchart. Shade in correct area.
Step 2: Graph y ≥ x² - 2x – 2. Vertex & tchart. Shade in correct area.
Find vertex, make t-chart &
y < -x² - x + 2
graph:
y ≥ x² - 2x – 2
Step 3: Identify the shaded region where
the two graphs overlap.
a) Solve x² - 5x ≤ - 4 algebraically.
First replace ≤ with =.
x² - 5x = - 4
x² - 5x + 4 = 0
Factor.
(x – 4)(x – 1) = 0
x = 4, 1
• The numbers 4 & 1 are the critical xvalues of the inequality. Plot 4 and 1 on
a number line using closed dots. Test
an x-value in each interval to see if it
satisfies the inequality.
• The solution is 1 ≤ x ≤ 4.
Solve algebraically:
1. x² - 3x – 18 ≤ 0
b) Solve x² - 11x +24 ≤ 0
graphically.
c) Solve 2x² - 18 > 0 graphically.