1. Warm Up
Write as an inequality and interval notation.

2. Graphs of Quadratic Inequalities
I can graph and find the solution set of quadratic inequalities.

3. Remember having to graph

4. Remember having to graph

5. Steps for Graphing (quickly)
Graph the quadratic (use your calculator for points)
For <> use DASHED for ≤≥ use SOLID line
Locate the roots/solutions of the quadratic
4. Shade the appropriate region using a test point

6. Graph: y ≤ x2 + 6x – 4 * Vertex: (-3,-13) * Solid Line
* Roots: X = {-6.6, 0.6}
* Interval Notation:

7. Graph: y > -x2 + 4x – 3 Vertex: Solid or Dotted: Roots: Test Point:
Interval Notation:

8. Graph: y ≥ x2 – 8x + 12 Vertex: Solid or Dotted: Roots: Test Point:
Interval Notation:

9. Graph: y > -x2 + 4x + 5 Vertex: Solid or Dotted: Roots: Test Point:
Interval Notation:

10. Warm Up Pass HW forward Factor and solve: 1. x2 – 5x = – 4
2. -x2 + 7x = 12 (hint: use rooftop)
Sketch the graph
-(x – 1)2 – 3

11. Solving a Quadratic Inequality

12. Steps for solving Write the original inequality as an equation
Set equal to 0, factor, and solve.
Plot the points on a number line and test points in each interval back into the original inequality.
Write the answer (the TRUE part) as an inequality

13.   Solve: x2 – 5x ≤ – 4 x2 – 5x = -4 x2 – 5x + 4 = 0
False
True  
False
Answer: 1 ≤ x ≤ 4
Interval Notation:

14. Solve: -x2 + 7x < 12 -x2 + 7x = 12 -x2 + 7x – 12 = 0
False
True
True  
Answer: x < 3 or x > 4
Interval:

15. What if it can’t factor? Graph it!

16. Solve: -(x – 1)2 – 3 < 0 -(x – 1)2 – 3 < y y > -(x – 1)2 – 3
Answer: all real numbers

17. Solve: x2 + 4 ≤ 0
x2 + 4 ≤ y
y ≥ x2 + 4
Answer: no solution