Warm up 9/09
Solve
1. x2 + 9x + 20 = 0
20
4
5
9
2. x2 - 7x = - 12
( x  4)( x  5)  0
x  4 or x  5
( x  3)( x  4)  0
x  3 or x  4
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
Be seated before the bell rings
Agenda:
DESK
homework
Warm-up (in
your notes)
Warmup
Go over hw
Notes 5.6
Ch 5 test tues 9/15
Notebook
1
Table of content
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
Page
1
12) 5.6 Quadratic
Formula
5.6 Quadratic Formula
ax2 + bx + c = 0
Use the quadratic formula to solve 5x2 + 6x = 2
Steps
1. Rearrange to standard form
2. Identify the a , b , c
3. Substitute into quad. formula
5x2 + 6x -2 = 0
a = 5 b= 6 c=-2
6  62  4  5 2 
2  5
4. Solve/simplify
6  76
10
6  2 19
10
6  76
10
6  76
10
6  2 19
10
Completing the Practice
• Use the quadratic formula to solve the
practice problem: x2 + 5x + 6
5  52  4(1)(6)
x
2(1)

5  1

2
5  1

2
4
2
 2
6

2
 3
Turn and Talk: Compare your answer by
factoring the quadratic and solving for x.
The Discriminant
b2 – 4ac
1. Positive  2 real solutions
Example: x2 + 10x – 5 = 0
2. Zero  1 real solution
Example: x2 + 4x + 4 = 0
3. Negative  No Real Solutions (2 complex solutions
Example: 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
82  4(1)(16)  0
1 solution
82  4(1)(10)  64  40  24
2 solutions
52  4(1)(7)  25  28  3
no real solution
Complex Solutions


2
1
i = √-1
 1
i let’s us rewrite square roots without a
negative number.
Example: √-4 = (√4)(√-1) = 2i
Turn and Talk: Show and explain how to
rewrite
√-81 using i
81 1  9 1
 9i
More practice with rewriting
A)
12
B ) 2 36
12  1
2 36  1
4  3  1
2  6  1
2 3  1
12 1
2 3 i
12i
An complex number has two parts
Finding the complex zeros of Quadratic Function
x2 –2x + 5 = 0
x
  2  
 2   4(1)(5)
2
2(1)
2  4i

2
 1  2i
2  16

2
2  16 1

2
Quadratic formula Practice
• In pairs,
Find the complex zeros of each.
1. x2 + 10x + 35 = 0
2. x2 + 4x + 13 = 0
 5  10i
3. x2 - 8x = -18
 4  34
 2  3i
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