Warm up 9/09Solve

  1. x2 + 9x + 20 = 0 2. x2 - 7x = - 12   

Turn and Talk• What were the different strategies you used to solve

each problems?

• Is completing the square or factoring easier for you? Why?

Shared

20

9

4 5

( 4)( 5) 0

4 or 5

x x

x x

( 3)( 4) 0

3 or 4

x x

x x

Be seated before the bell rings

DESK

homeworkWarm-up (in your notes)

Ch 5 test tues 9/15

Agenda:

WarmupGo over hw

Notes 5.6

NotebookTable of content

Page1

1

7) 2.3 & 2.4

10) /5.3 Solve quadratics by factoring

11) 5.4 Solve Quadratics by Completing the Square

12) 5.6 Quadratic Formula

12) 5.6 Quadratic Formula

● 5.4: I can solve a quadratic equation by using

square roots

● 5.4: I can solve a quadratic equation by using the

complete the square method.

● 5.4: I can re-write a quadratic function in vertex

form by completing the square.

● 5.6: I can find the zeros/solutions of a quadratic

equation using the quadratic formula

Learning Targets

ax2 + bx + c = 0

Use the quadratic formula to solve 5x2 + 6x = 2

Steps1.Rearrange to standard form2.Identify the a , b , c 3.Substitute into quad. formula

4.Solve/simplify

5.6 Quadratic Formula

5x2 + 6x -2 = 0a = 5 b= 6 c=-2

26 6 4 5 2

2 5

6 76

10

6 76

10

6 76

10

6 2 19

10

6 2 19

10

Completing the Practice• Use the quadratic formula to solve the

practice problem: x2 + 5x + 6

Turn and Talk: Compare your answer by factoring the quadratic and solving for x.

25 5 4(1)(6)

2(1)x

5 1

2

5 1

2

4

2

6

2

2

3

The Discriminant

b2 – 4ac1. Positive 2 real solutions

Example: x2 + 10x – 5 = 0

2. Zero 1 real solutionExample: x2 + 4x + 4 = 0

3. Negative No Real Solutions (2 complex solutionsExample: 5x2 + 2x + 4 = 0

Turn and Talk: Why is √-80 not a real solution?

Practice

• Show and Explain how many solutions the following quadratic equations will have?

1. x2 + 8x + 16 = 0

2. x2 + 8x + 10 = 0

3. x2 + 5x + 7 = 0

28 4(1)(16) 0 1 solution

28 4(1)(10) 64 40 24 2 solutions

25 4(1)(7) 25 28 3

real solutionno

Complex Solutions

i = √-1

i let’s us rewrite square roots without a negative number.

Example: √-4 =

Turn and Talk: Show and explain how to rewrite √-81 using i

(√4)(√-1) = 2i

2

1 1

81 1 9 1 9i

More practice with rewriting

) 12A

12 1

4 3 1

2 3 1

2 3 i

) 2 36B

2 36 1

2 6 1

12 1

12i

An complex number has two parts

Finding the complex zeros of Quadratic Function

x2 –2x + 5 = 0

22 2 4(1)(5)

2(1)x

2 16

2

2 16 1

2

2 4

2

i 1 2i

Quadratic formula Practice

• In pairs,

Find the complex zeros of each.

1. x2 + 10x + 35 = 0 2. x2 + 4x + 13 = 0

3. x2 - 8x = -18

5 10i 2 3i

4 34

Closer : Summarize:Write down one different thing each group member learn today into your notes.

http://www.showme.com/sh/?h=eeY9fKi

Additional Practice

Quadratic formula Practice• In pairs,

1.Solve using the quadratic formula

1. x2 + 5x + 3 = 0

2. 3x2 + 10x + 7 = 0

3. x2 + 11x = -6

4. x2 + 10x = 200