algebra ch. 10.8 discriminant of quadratic...
TRANSCRIPT
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Algebra – Ch. 10.8Discriminant of Quadratic Formula
Mr. Deyo
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Learning Target
By the end of the period, I will interpret the discriminant to determine the number of roots in a given quadratic equation.
I will demonstrate this by completing Four-Square Notes and by solving problems in a pair/group activity.
Title: 10.8 Interpret the Discriminant Date:
![Page 3: Algebra Ch. 10.8 Discriminant of Quadratic Formulahelpmeteach.weebly.com/uploads/1/7/1/0/17102056/____ms_algebra_… · Algebra –Ch. 10.8 Discriminant of Quadratic Formula Mr. Deyo](https://reader030.vdocuments.site/reader030/viewer/2022021612/5b931e0709d3f27f5d8c8630/html5/thumbnails/3.jpg)
Home Work 1-2-3: 1) Class 4-Square Notes Put In Binder?
2) Section 10.8 Pg. 660 3) Section ______
TxtBk. Problems #3-19 Odd Notes Copied on blank sheet Solved and Put in Binder? of paper in Binder?
Table of ContentsDate Description Date Due
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Storm Check (Think, Write, Discuss, Report)
Questions on which to ponder and answer:1. How are the two images similar?
2. How are they different?
3. How can these two images be related to math?
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1) Discriminant
2) Quadratic Formula
3) Quadratic Equation
4) Roots
Vocabulary
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DAY 3 and/or DAY 4
1. Review the word
Friendly Definition
Physical Representation
2. Show how the word works
Synonyms/antonym
Word Problems
Related words/phrases
Example/non-example
Friendly DefinitionSketch
Wordwork Sentence
DAY 2
1. Review word
Friendly Definition
Physical Representation
2. Draw a sketch
DAY 5
1. Review the word
Friendly definition
Physical Representation
3. Write a sentence
at least 2 rich words (1 action)
correct spelling
correct punctuation
correct subject/predicate agreement
clear and clean writing
DAY 1
1. Use Visuals
2. Introduce the word
Friendly Definition
Physical Representation
3. Use Cognates
4. Write friendly definition
5. Physical Representation
Word List1.2.3.4.
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Use the discriminantProblem A
Number of
solutions
x2 7 = 0– 12x4x2 9+ = 0–
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Use the discriminantProblem A
Number of
solutions
x2 7 = 0–
(14 )02 – = 28( )7– – )9((44 ) = 0( )212–
12x4x2 9+ = 0–
Two
solutions
One
solution
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Use the discriminantProblem B
Number of
solutions
10x+x2 25+=y 6x+2x2 5+ =0
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Use the discriminantProblem B
Number of
solutions
10x+x2 25+=y
102 -4(1)(25) =
100 – 100 = 0
One
solution
6x+2x2 5+ =0
)5((24 )62– = 4–
No
solutions
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The value of is equal to 0.
Which statement best explains why there is only one
real solution to the quadratic equation ?
The value of is positive.
Multiple Choice PracticeCST
6x+9x2 1+ = 0
(6)2 94 • 1•–
(6)2 94 • 1•–
The value of is negative.(6)2 94 • 1•–
The value of is not a perfect
square.(6)2 94 • 1•–
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SOLUTION
Find the value of the discriminant.
ANSWER The correct answer is B.
Multiple Choice PracticeCST
b2 a4 • c•– = (6)2 94 • 1•– 36 36–= 0=
The discriminant is zero, so the equation has one real
solution.
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Storm Check (Think, Write, Discuss, Report)
What is the purpose of calculating the value of the discriminant?
The purpose of calculating the discriminant is
_______________________________________
_______________________________________.
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Problem A
Find the number of x-intercepts of the graph of
Find the number of x-intercepts
3xx2 10.= – –y
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Problem A
Find the number of x-intercepts of the graph of
Find the number of x-intercepts
3xx2 10.= – –y
SOLUTION
Find the number of solutions of the equation
3xx2 10.= – –0
(14 )–( )23– ( )10–4acb2– = Substitute 1 for a, for b,
and for c.
3–10–
49= Simplify.
The discriminant is positive, so the equation has two
solutions. This means that the graph of
has two x-intercepts.3xx2 10= – –y
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Prob. A Ck. Find the number of x-intercepts
CHECK You can use a graphing calculator to check
the answer. Notice that the graph of
has two x-intercepts.3xx2 10= – –y
You can also use factoring
Because the
graph of crosses the x-axis at
or and at or
( )x – 5 ( ),x + 23xx2 10 =– –3xx2 10– –y =
–x 5 = 0, x = 5, +x 2 = 0, x = – 2.
to check the answer.
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Guided Practice
Find whether the equation has two solutions (2), one solution
(1), or no solutions (0).
4x+x2 3+ = 0 5x2x2 6+ = 0–
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Guided Practice
Find whether the equation has two solutions (2), one solution
(1), or no solutions (0).
4x+x2 3+ = 0
ANSWER
No solutions (0)
5x2x2 6+ = 0–
Two solutions (2)
ANSWER
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Storm Check (Think, Write, Discuss, Report)
How does the value of the discriminant relate the number of times a parabola crosses the x-axis? Explain.
The value of the discriminant relates to the number
of times a parabola crosses the x-axis in three ways:
1) _______________________________________.
2) _______________________________________.
3) _______________________________________.
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1) Discriminant
2) Quadratic Formula
3) Quadratic Equation
4) Roots
Vocabulary
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Home Work 1-2-3: 1) Storm Check Pasted in Notebook?
2) Section ______ 3) Section ______
Txtbk Problems_________ Notes Copied in Notebook? Pasted & Solved in Notebook?
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Learning Target
By the end of the period, I will interpret the discriminant to determine the number of roots in a given quadratic equation.
I will demonstrate this by completing Four-Square Notes and by solving problems in a pair/group activity.
Title: 10.8 Interpret the Discriminant Date:
![Page 23: Algebra Ch. 10.8 Discriminant of Quadratic Formulahelpmeteach.weebly.com/uploads/1/7/1/0/17102056/____ms_algebra_… · Algebra –Ch. 10.8 Discriminant of Quadratic Formula Mr. Deyo](https://reader030.vdocuments.site/reader030/viewer/2022021612/5b931e0709d3f27f5d8c8630/html5/thumbnails/23.jpg)
Ticket OUT.
Find the number of x-intercepts of the graph of the function.
9xx2 –=y 2x+x2–=y 4–
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Ticket OUT.
ANSWER ANSWER
Find the number of x-intercepts of the graph of the function.
9xx2 –=y 2x+x2–=y 4–
2 0