Graphing Quadratic Inequalities

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9.6

• Graphing Quadratic Inequalities

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Sketch the graph of 6x 5y 30
Remember how to graph a linear inequality?

• Write in slope- intercept form
• y -6/5x 6
• This will be a solid line.
• Test a point. (0,0)6(0) 5(0) 300 30 Not
  a solution.
• Shade the side that doesnt include (0,0).

6 4 2
2 4 6 8
-6 -4 -2
-2 -4 -6
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Rules for Graphing Quadratic Inequalities
1. Sketch the graph of the parabola yltax2bxc
use ------ line for lt, gt

use ______ line for
2. Test points inside the U shape and one outside
the U shape.
3. Shade the region that contains the solution.
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2
Check discriminant first for number of solutions
b2-4ac
(-2)2-4(3)(4)
4-48
-44
NO SOLUTION Quadratic equation wont work for
x-axis crossings.
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Next Step y 3x2 2x 4
Find a vertex, then make a table.
-b2a -(-2)2 3 26
The x-coordinate of the vertex is 1/3.
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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
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Make a table of values to find points left and
right of the vertex.
x 3x2 2x 4 y (x, y)
-1 3(-1)22(-1) 4 9 (-1, 9)
Vertex (1/3, 11/3)
2 3(2)2 - 2(2) 4 12 (2, 12)
Now sketch the graph.
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y 3x2 2x 4
y
8
Solid line
6
4
2
x
-2
-4
-6
4
6
8
-2
2
-4
-6
-8
9
In (0,6)
Out (0,0)
Check Point
2
2
Yes
NO
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Final Graph
y
8
2
6
4
2
x
-2
-4
-6
4
6
8
-2
2
-4
-6
-8
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Try this one

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