Algebra Ch. 10.8 Discriminant of Quadratic...

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