Dispatch Monday 2/25/13 Simplify 2. – 6 ÷12 – 0.5 3. The length of the side of a square is 4x...
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Transcript of Dispatch Monday 2/25/13 Simplify 2. – 6 ÷12 – 0.5 3. The length of the side of a square is 4x...
DispatchMonday 2/25/13Simplify
3
1.
2. – 6 ÷12
– 0.5
3. The length of the side of a square is 4x – 5 . What is the area of the square?
16x2 – 40x + 25
4. m2 – 10m + 25
(m – 5)2
Factor
Solving Quadratic Equations by Completing the Square
Do you remember….What are the properties of a square?
Standard: 14.0
CONCEPT TASK
CONCEPT TASK
x
x A = x2 x
1
1
x2 x
COPY ME!!!
Represent the Expression:x2 + 3x + 6
CONCEPT TASK
x2 + 4x + 4
2x2 + 3x – 4
– 3x2 + 3x – 4 WORK WITH YOUR
PARTNERS
CONCEPT TASK
x2 + 4x + 4
CONCEPT TASK
2x2 + 3x – 4
CONCEPT TASK
2x2 + 3x – 4
CONCEPT TASK
– 2x2 – 3x + 4
CONCEPT TASK
– 2x2 – 3x + 4
CONCEPT TASK
Using ONLY the Algebra tiles below, create a square.
CONCEPT TASKWhat do you do to complete the square x2
+ 2x + ___
CONCEPT TASKHow many 1-unit tiles do you need to add to complete the square? x2 + 2x + ____
CONCEPT TASKHow many 1-unit tiles do you need to add to complete the square? x2 + 2x + ____1
CONCEPT TASKHow many 1-unit tiles do you need to add to complete the square? x2 + 2x + ____1
x + 1
x + 1
x + 1
x + 1
Completing the Square
Expression Number of 1-tiles needed to be
added to complete the
square
What is the Area of your
Square?
A. x2 + 2x + ? (x + ____ )2
B. x2 + 4x + ?
C. x2 – 6x + ?
D. x2 + 8x + ?
CONCEPT TASKWhat do you do to complete the square x2
+ 4x + ___
CONCEPT TASKWhat do you do to complete the square x2
+ 8x + ___
CONCEPT TASKWhat do you do to complete the square x2
– 6x + ______
CONCEPT TASKNow arrange your tiles to make a perfect square
CONCEPT TASKHow many 1-unit tiles do you need to add to complete the square? x2 - 6x + ______9
CONCEPT TASK
x - 3
x - 3
x - 3x - 3
CONCEPT TASK
x - 3
x - 3
x - 3x - 3
Area= l ● wA = (x-3)(x-3)A=(x - 3)2
CONCEPT TASKx2 - 6x + 9 = (x - 3)2
Completing the Square
Expression Number of 1-tiles needed to be
added to complete the
square
What is the Area of your
Square?
A. x2 + 2x + ? 1 (x + 1 )2
B. x2 + 4x + ? 4 (x + 2)2
C. x2 – 6x + ? 9 (x – 3)2
D. x2 + 8x + ? 16 (x + 4)2
What is the relationship between the values in Column 2 and 3 and the coefficient of the linear term? What were the steps you took in order to complete the square?
THINK PAIR SHARE
Let’s try without algebra tiles
Find the missing value. s2 -16s + _
Step 1: Divide b by 2
Step 2: Square the result of step 1
Step 3: Add the result to the original expressionStep 4: Factor (x + )2
- = -8
(-82 ) = 64
s2 -16s + 64
COMPLETE THE SQUARE
x2 + 22x + ___= (x + ___ )2
x2 – 16x + ___= (x – ___ )2
x2 + 12x + ___= (x + ___ )2
COMPLETE THE SQUARE
x2 + 5x + ___= (x + ___ )2
g2 + 11g + ___=
p2 – 9p + ___=
COMPLETE THE SQUARE
m2 – 1.8m + ___= (x – ___ )2
y2 + y+ ___=
x2 – x + ___=
CONCEPT TASK
JOURNAL:Your best friend was absent today. Write your friend a letter explaininghow to complete the square using algebra tiles and how to do it withoutusing algebra tiles
COMPLETE THE SQUARE
Daily Practice
• Skills Practice Pg 59 7-12• Pg 735 Lesson 9-3
7-12
DispatchTuesday 2/26/13Find the value of c that makes the trinomial a perfect square. (Use Algebra Tiles and solve Algebraically)
1. x2 – 10x + c
VISUALLY x - 5
x - 5x - 5
x - 5
Area= l ● wA = (x-5)(x-5)A=(x - 5)2
Find the missing value. x2 –10x + _____
Step 1: Divide b by 2
Step 2: Square the result of step 1
Step 3: Add the result to the original expressionStep 4: Factor (x + )2
= – 5
(– 52 ) = 25
x2 – 10x + 25
(x – 5)2
ALGEBRAICALLY
DispatchThursday 2/28/13Solve the Equation.
1. x2 – 2x + 1 = 25
x = – 4 and 6
16 2. m2 – 8m + 16
(m – 4)2
Factor
Find the value of c that makes the trinomial a perfect square .
3. x2 + 8x + c
Solving Quadratic Equations by Completing the Square
Do you remember….What are the other methods for solving quadratic equations?
Standard: 14.0
CONCEPT TASK
CONCEPT TASK
x
x A = x2 x
1
1
x2 x
1. x – 5 = 2
x – 5 = 2
1. x – 5 = 2
x – 5 = 2
1. x – 5 = 2
x – 5 = 2
1. x – 5 = 2
x = 7
YOUR TURN
1. x + 6 = – 4
2. 2x – 4 = – 8
3. x2 + 4x = 2
1. x + 6 = – 4
x = – 2
1. 2x – 4 = – 8
x = 4
x2 + 4x = 5
x + 2
x + 2
x + 2
x2 + 4x + 4 = 9
(x + 2)2 = 9
Step 2: Take the square root of each side to cancel the square.Step 3: Solve One-Step Equation.
(m + 2)2 = 9
m + 2 =
m = – 2 Step 4: Split Up
(x + 2)2 = 9
m = – 2
m= – 2 + 3 m= – 2 – 3
m= 1 m= – 5
Challenge: Is there a faster method to complete the
square without using Algebra Tiles? Write in complete
sentences
Thin
k Pa
ir Sh
are
YOUR TURN
Solve the equation using completing the square. Represent your answer both Visually with Algebra Tiles and Algebraically.
x2 + 6x = 2
q2 – 2q = 16
1. x2 + 4x + 3 = 0
x2 + 4x + 3 = 0
x2 + 4x + 3 = 0
x2 + 4x + 3 = 0
x2 + 4x + 3 = 0
x2 + 4x + 3 = 0
(x + 2)2 = 1
Step 2: Take the square root of each side to cancel the square.Step 3: Solve One-Step Equation.
(x + 2)2 = 1
x + 2 =
x = – 2 Step 4: Split Up
(x + 2)2 = 1
x = – 2
x= – 2 + 1 x= – 2 - 1
x= -1 x= – 3
Thin
k Pa
ir Sh
are
YOUR TURN x2 – 4x – 5 = 0
x2 – 14x + 30 = 6
x2 + 14x + 49 = 10
Daily Practice
I want you to create your own Completing the Square Problem. Make sure you represent it using Algebra Tiles and algebraically. Make a key and be ready to share the problem with your partners tomorrow.
Study Guide and Intervention Pg 118 #1-18 ODD (Skip 11)