algebra ch. 10.8 discriminant of quadratic...
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Algebra – Ch. 10.8Discriminant of Quadratic Formula
Mr. Deyo
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:
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
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?
1) Discriminant
2) Quadratic Formula
3) Quadratic Equation
4) Roots
Vocabulary
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.
Use the discriminantProblem A
Number of
solutions
x2 7 = 0– 12x4x2 9+ = 0–
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
Use the discriminantProblem B
Number of
solutions
10x+x2 25+=y 6x+2x2 5+ =0
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
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•–
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.
Storm Check (Think, Write, Discuss, Report)
What is the purpose of calculating the value of the discriminant?
The purpose of calculating the discriminant is
_______________________________________
_______________________________________.
Problem A
Find the number of x-intercepts of the graph of
Find the number of x-intercepts
3xx2 10.= – –y
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
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.
Guided Practice
Find whether the equation has two solutions (2), one solution
(1), or no solutions (0).
4x+x2 3+ = 0 5x2x2 6+ = 0–
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
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) _______________________________________.
1) Discriminant
2) Quadratic Formula
3) Quadratic Equation
4) Roots
Vocabulary
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?
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:
Ticket OUT.
Find the number of x-intercepts of the graph of the function.
9xx2 –=y 2x+x2–=y 4–
Ticket OUT.
ANSWER ANSWER
Find the number of x-intercepts of the graph of the function.
9xx2 –=y 2x+x2–=y 4–
2 0