Warm Up

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Warm Up
Write as an inequality.
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Remember having to graph
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Remember having to graph
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Graphing Quadratic Inequalities

• Lesson 3.9

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Steps for Graphing (quickly)

• Graph the vertex
• Use the slope (1, 3, 5) to get the other points
  (if a 1)
• For ltgt use DASHED for use SOLID line
• 4. Shade the appropriate region (greater shade
  above the vertex, less shade below the vertex)

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Shading
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Graph y x2 6x 4
Vertex (-3,-13)
Slope 1, 3, 5
Solid Line
Less than means shade BELOW
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Graph y gt -x2 4x 3
Vertex (2, 1)
Slope -1, -3, -5
Dashed Line
Greater than means shade ABOVE
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Graph y x2 8x 12
Vertex (4, -4)
Slope 1, 3, 5
Solid Line
Greater than means shade ABOVE
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Graph y gt -x2 4x 5
Vertex (2, 9)
Slope -1, -3, -5
Dashed Line
Greater than means shade ABOVE
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Solving a Quadratic Inequality
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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

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Solve x2 5x 4
x2 5x -4
x2 5x 4 0
(x 4) (x 1) 0
x 1, 4
False
?
?
True
False
Answer 1 x 4
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Solve -x2 7x lt 12
-x2 7x 12
-x2 7x 12 0
x2 7x 12 0
(x 4) (x 3) 0
x 3, 4
False
True
True
?
?
Answer x lt 3 or x gt 4
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What if it cant factor?Graph it!
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Solve -(x 1)2 3 lt 0
-(x 1)2 3 lt y
y gt -(x 1)2 3
Answer all real numbers
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Solve x2 4 0
x2 4 y
y x2 4
Answer no solution
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Workbookp. 110 13 18
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HW Textbookp. 98 1 18p. 99 28, 31
33(solve algebraically)