Do Now

Find the square roots

1. √16 2. √363. √814. √495. √-256. √32

When it’s hip to “b2”

Given quadratic equations, students will find solutions using

the quadratic formula.

Quadratic formula:

X = b b2 4ac

2a

x = 3 +/- √16

x = 3 +/- 4

x = 3 + 4 x = 3 – 4

= 7 = -1

x = 1 +/- √25

x = 1 +/- 5

x = 1 + 5 x = 1 – 5

= 6 = -4

2

15x

x = -5 +/- 1 2

x = -5 + 1 x = -5 - 1 2 2

x = -4 x = -6 2 2

x = -2 x = -3

16

1002x

(I DO) Simplify:

8 +/- √48

4

8 +/- 4√3

4

2 +/- √3

√48

√16 √3

4 √3

Simplify:

1. 4 +/- √50 2. 3 +/- √32

2 4

3. -8 +/- √48 4. -1 +/- √14

6 -6

Quadratic Formula

Now let’s try plugging in the information and simplify.

SOLVE:

1. 5x2 + 3x - 1 = 0

2. 2x2 - 7x + 2 = 0

RESPONSE CARDS Simplify:

-8 +/- √48

6

Can this be simplified?Thumbs up or down

3 +/- √32

4

RESPONSE CARDS Simplify:

2 +/- √33

4

RESPONSE CARDS Simplify:

-1 +/- √14

-6

Tell your partner what are the 4 ways to find a solution to a

quadratic equation?

• 1. Graphing

• 2. X-Puzzle (Factoring)

• 3. Square Root

• 4. Completing the square

Given: 2x2 - 5x + 4 = 0

How do we find the solutions?

8

-5

NO ANSWER! What do we do?

Quadratic formula:

X = b b2 4ac

2a

• A negative boy• Wasn’t sure whether or not• To go to this radical party• Instead the boy was square• And he missed out on 4

awesome chicks

• But it was all over at 2 am

The Party

- b

A negative boy

±

Wasn’t sure whether or not

√

To go to this radical party

b

Instead he was square

²

- 4ac

And he missed out on 4 awesome

chicks

2a

But it was all over at 2 am

When do we use the Q.F.?

When trying to find solutions:

First try: x - puzzle

- Uh oh! x-puzzle doesn’t work!

Second try: quadratic formula

Write a sentence in your own words describing when to use the Q.F.

Example 1: 2x2 - 5x + 4 = 0a = 2 b = -5 c = 4

b b2 4ac2a

(-5)2 (2)(4)

(2)

-(-5)

Example 3: 5x2 + 4x - 2 = 0

a = 5 b = 4 c = -2

b b2 4ac2a

(4)2 (5)(-2)

(5)

-(4)

Example 2: 2x2 - 8x + 1 = 0a = 2 b = -8 c = 1

b b2 4ac2a

(-8)2 (2)(1)

(2)

-(-8)

b b2 4ac2a

-(-8) (-8)2 (2)(1)

(2)

8 56

4

8 64 84

82 144

4 14

2

Solutions!

Quadratic Formula Comic

• Fold paper into 6 boxes

• Each box is part of the quadratic formula

• Draw a picture to represent each part of the party

• Due by Thurs/Friday

Example 4: 3x2 - 5x + 1 = 0

a = 3 b = -5 c = 1

b b2 4ac2a

(-5)2 (3)(1)

(3)

-(-5)

T.O.D.

1. Simplify: 4 +/- √24

2

2. Write the quadratic formula.

ALGEBRA 1P GAME PLAN

Date 3/23/11 Wednesday

Section / Topic Notes #118: 9-7a: Quadratic formula

Lesson Goal STUDENTS WILL SIMPLIFY RADICALS & KNOW THE QUADRATIC FORMULA ON A T.O.D.

Algebra California Standard

19.0 Students know the quadratic formula and are familiar with its proof by completing the square.

Homework#118

COPY THE QUADRATIC FORMULA ? X

Announcements

• Chapter 9 Quadratics Test: Next Wed, 3/30

Do Now

1. What are the solutions of 5x2 + 6x = - 1?

2. What are the x-intercepts of 2x2 – 5x + 4 = 0?