Download Quadratic Inequalities

Quadratic Inequalities
Lesson 3.4
Definition
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Recall the quadratic equation
ax2 + bx + c = 0
Replace = sign with <, >, ≤, or ≥ makes it a
quadratic inequality
Solving:
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Find where the equality occurs
These values are the boundary numbers
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Graphical Solutions
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Graph of the quadratic y = ax2 + bx + c is a
parabola
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Extends upward or downward
Solution to y > 0 includes all
x-values where graph is
above the axis
Solution to y < 0 includes
x-values where graph is
below the axis
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Try It Out
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Given 2 x  5 x  2  0
Place in Y= screen, graph
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3.14  x  0.64
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Determine boundary values (zeros of equation)
Which values of x satisfy the inequality?
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Another Version
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Consider 2x2 > 16
Create a graph of both sides of the inequality
Determine values of x which satisfy the
equation, then the inequality
x  2 2
or
x2 2
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Steps for Symbolic Solution
1. Write as an equation ax2 + bx + c = 0
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Solve resulting equation for boundary numbers
2. Use boundary numbers to separate number
line into disjoint intervals
3. Make a table of test values
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One value from each interval
4. Use this to specify which intervals satisfy the
original inequality
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Example
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Try x2 – 9 < 0
Solve x2 – 9 = 0
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x = +3 or x = -3
x
y
•
•
-5
16
-2
-5
This is the interval
7
40
3  x  3
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Using the Calculator Table
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Place function in the
Y= screen
Go to Table, ♦Y
Adjust start, increment
as needed, F2
View intervals where
results are
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negative,
zero,
or positive
x2 – 9 < 0
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Assignment
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Lesson 3.4
Page 218
Exercises 1 – 53 EOO
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