Algebra II Mr. Gilbert

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Algebra IIMr. Gilbert

• Chapter 6.2
• Solving Quadratic Functions by Graphing
• Standard Honors

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Agenda

• Warm up
• Homework
• Check your answers
• Applet
• Lesson

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Lesson 2 Contents
Solving Quadratic Functions by Graphing
Example 1 Two Real Solutions (4) Example 2 One
Real Solution (3) Example 3 No Real Solution
(4) Example 4 Estimate Roots (3) Example 5 Write
and Solve an Equation (5)
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Example 2-1a
x 1 0 1 2 3 4
f (x) 0 4 6 6 4 0
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Example 2-1a
From the table and the graph, we can see that
the zeroes of the function are 1 and 4.
Answer The solutions of the equation are 1 and
4.
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Example 2-1a
Check Check the solutions by substituting each
solution into the original equation to see if it
is satisfied.
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Example 2-1b
Answer
3 and 1
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Example 2-2a
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Example 2-2a
Notice that the graph has only one x-intercept,
2.
Answer The equations only solution is 2.
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Example 2-2b
Answer 3
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Example 2-3a
Number Theory Find two real numbers whose sum
is 4 and whose product is 5 or show that no such
numbers exist.
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Example 2-3a
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Example 2-3a
Notice that the graph has no x-intercepts. This
means that the original equation has no real
solution.
Answer It is not possible for two numbers to
have a sum of 4 and a product of 5.
Examine Try finding the product of several
numbers whose sum is 4.
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Example 2-3b
Number Theory Find two real numbers whose sum
is 7 and whose product is 14 or show that no
such numbers exist.
Answer no such numbers exist
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Example 2-4a
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Example 2-4a
The x-intercepts of the graph are between 0 and 1
and between 5 and 6.
Answer One solution is between 0 and 1 and the
other is between 5 and 6.
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Example 2-4b
Answer between 0 and 1 and between 3 and 4
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Example 2-5a
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Example 2-5a
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Example 2-5a
Answer The positive zero of the function is
approximately 8. It should take about 8 seconds
for the marble to reach the surface of the water.
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Example 2-5b
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Example 2-5b
Answer about 7 seconds
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Homework Review
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Homework - Honors
See Syllabus 6.2 pp. 297-298 15-36 (multiples of
3), 38-47
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Homework
See Syllabus 6.2 pp. 297 299 14-19,20-36
even,38-46