Download Chapter 6

Warm-up
• Solve the following two quadratic equations
by using the Square Roots Method:
• 4x2 – 8 = 12
• (x - 3)2 - 7 = - 15
Warm-up
• 4x2 – 8 = 12
• 4x2 = 20
• x2 = 5
x 5
Warm-up
• (x – 3)2 - 7 = - 15
• (x – 3)2 = -8
x  3   8
x  3 2 2 i
Chapter 4
Section 4-7
Completing the Square
Vertex Format
Objectives
• I can complete the square to
find Vertex Format of a
quadratic equation
A Perfect Square
• A perfect square is a trinomial expression
that has 2 factors that are the same:
• Example: (x2 + 10x + 25) is a perfect
square with factors
• (x + 5)(x + 5)
Special Factoring
• x2 + 18x + 81 = 0
• (x + 9)(x + 9) = 0
• (x + 9)2 = 0
• x2 – 8x + 16 = 0
• (x –4)(x – 4) = 0
• (x – 4)2 = 0
• This was a perfect
square
• Again, a perfect
square
Making a Perfect Square
• Consider the following equation:
• x2 + 14x + c = 0
• What number does c need to be to make a
perfect square?
• Follow the procedure on next slide.
Perfect Square Method
•
•
•
•
•
•
•
•
x2 + 14x + c
Take middle term and divide by 2
14/2 = 7
Next square the results
72 = 49
x2 + 14x + 49
(x + 7)(x + 7)
(x + 7)2
Another Example
•
•
•
•
•
•
•
x2 – 8x + c
Take middle term and divide by 2
-8/2 = - 4
Now square that new number
(-4)2 = 16
x2 – 8x + 16
(x – 4)2
You can get fractions
•
•
•
•
•
•
•
x2 – 5x + c
Take middle term and divide by 2
-5/2 = - 5/2
Now square that new number
(-5/2)2 = 25/4
x2 – 8x + 25/4
(x – 5/2)2
Teeter-Toter
Keeping Balanced
+20
+20
Vertex Format
• y = a(x – h)2 + k
• Vertex Point: (h, k)
Converting to Vertex
•
•
•
•
•
•
•
•
y = x2 +8x + 10
y = (x2 + 8x) + 10
y = (x2 + 8x + _____) + 10
y + 16 = (x2 + 8x + 16) + 10
y + 16 = (x + 4)(x + 4) + 10
y + 16 = (x + 4)2 + 10
y = (x + 4)2 - 6
Vertex Point (-4, -6)
Converting to Vertex
•
•
•
•
•
•
•
•
•
y = 2x2 +8x + 5
y = (2x2 + 8x) + 5
y = 2(x2 + 4x) + 5
y = 2(x2 + 4x + _____) + 5
y + 8 = 2(x2 + 4x + 4) + 5
y + 8 = 2(x + 2)(x + 2) + 5
y + 8 = 2(x + 2)2 + 5
y = 2(x + 2)2 - 3
Vertex Point (-2, -3)
Homework
• WS 6-3