warm up 9/09 solve 1. x 2 + 9x + 20 = 0 2. x 2 - 7x = - 12 turn and talk what were the different...
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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