1. Graphing Quadratic Inequalities
9.6
Graphing Quadratic Inequalities

2. Sketch the graph of 6x + 5y ≥ 30
Remember how to graph a linear inequality?
Sketch the graph of 6x + 5y ≥ 30
Write in slope- intercept form:
y ≥ -6/5x + 6
This will be a solid line.
Test a point. (0,0) 6(0) + 5(0) ≥ 30 0 ≥ 30 Not a solution.
Shade the side that doesn’t include (0,0). 6 4 2 -2 -4 -6

3. Rules for Graphing Quadratic Inequalities:
1. Sketch the graph of the parabola y<ax2+bx+c
use line for <, >
use ______ line for
2. Test points inside the U shape and one outside the U shape.
3. Shade the region that contains the solution.

4. 2
Check discriminant first for number of solutions
b2-4ac
(-2)2-4(3)(4)
4-48
-44
NO SOLUTION = Quadratic equation won’t work for x-axis crossings.

5. Next Step… y ≥ 3x2 – 2x + 4 Find a vertex, then make a table. -b 2a
-(-2) 2 ∙ 3
2 6
The x-coordinate of the vertex is 1/3.

6. Plug in 1/3 to original equation to find y value: y ≥ 3x2 – 2x + 4
3(1/3)2 – 2(1/3) + 4
3(1/9) – 2/3 + 4
1/3 – 2/3 + 4

7. Make a table of values to find points left and right of the vertex.
3x2 – 2x + 4 y
(x, y) -1
3(-1)2–2(-1) + 4 9
(-1, 9)
Vertex
(1/3, 11/3) 2
3(2)2 - 2(2) + 4 12
(2, 12)
Now sketch the graph.

8. y ≥ 3x2 – 2x + 4 y 8
Solid line 6 4 2 x -6 -4 -2 -2 2 4 6 8 -4 -6 -8

9. Check Point
Out
(0,0) In
(0,6) 2 2 NO
Yes

10. Final Graph y 8 2 6 4 2 x -6 -4 -2 -2 2 4 6 8 -4 -6 -8

11. Pick a point to the right and one to the left Graph
Try this one
y > -x2 + 2x – 1
Find the vertex
Pick a point to the right and one to the left
Graph
Shade (pick a point and shade the true side)
(1, 0)

12. Dotted line Shade outside y x 8 6 4 (1,0) -6 -4 4 6 8 -4 -6 -8 2 -2 -2