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