Algebra II Mr. Gilbert

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Algebra IIMr. Gilbert

• Chapter 6.7
• Graphing and Solving Quadratic Inequalities
• Standard Honors

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Agenda

• Warm up
• Homework Review
• Check your answers
• Lesson
• New Homework

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Transparency 7
Click the mouse button or press the Space Bar to
display the answers.
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Transparency 7a
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Homework Review
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Lesson 7 Contents
6.7 Graphing and solving Quadratic Inequalities
Example 1 Graph a Quadratic Inequality
(4) Example 2 Solve ax2 bx c ? 0 (3) Example
3 Solve ax2 bx c ? 0 (5) Example 4 Write an
Inequality (4) Example 5 Solve a Quadratic
Inequality (5)
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Example 7-1a
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Example 7-1a
Step 2Test a point inside the parabola, such as
(1, 2).
(1, 2)
So, (1, 2) is a solution of the inequality.
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Example 7-1a
Step 3 Shade the region inside the parabola.
(1, 2)
(1, 2)
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Example 7-1b
Answer
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Example 7-2a
The solution consists of the x values for which
the graph of the related quadratic function lies
above the x-axis. Begin by finding the roots of
the related equation.
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Example 7-2a
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Example 7-2b
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Example 7-3a
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Example 7-3a
Sketch the graph of the parabola that has
x-intercepts of 3.16 and 0.16. The graph should
open down since a lt 0.
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Example 7-3a
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Example 7-3a
Check Test one value of x less than 3.16, one
between 3.16 and 0.16, and one greater than 0.16
in the original inequality.
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Example 7-3b
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Example 7-4a
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Example 7-4a
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Example 7-4a
Answer Thus, the ball is within 15 feet of the
ground for the first 0.46 second of its flight
and again after 2.04 seconds until the ball hits
the ground at 2.5 seconds.
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Example 7-4b
Answer The ball is within 10 feet of the ground
for the first 0.5 second of its flight and again
after 1.25 seconds until the ball hits the ground.
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Example 7-5a
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Example 7-5a
Plot 2 and 1 on a number line. Use closed
circles since these solutions are included.
Notice that the number line is separated into 3
intervals.
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Example 7-5a
Test a value in each interval to see if it
satisfies the original inequality.
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Example 7-5a
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Example 7-5b
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Homework - Honors
See Syllabus 6.7 pp. 333-334 14, 24, 26, 28,
32-40 even 43-49
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Homework
See Syllabus 6.5 pp. 333-334 15 39 multiples
of 3