Completing the square

Intro Lesson
11:49
Lesson: 1a
2:25
Lesson: 1b
4:30
Lesson: 2a
1:05
Lesson: 2b
0:32
Lesson: 2c
1:49
Lesson: 2d
1:56
Lesson: 2e
3:00

Learn

Completing the square

Basic concepts: Factoring perfect square trinomials:

(a + b)^2 = a^2 + 2ab + b^2

(a - b)^2 = a^2 - 2ab + b^2

, Quadratic function in vertex form: y =

a(x-p)^2 + q

,

Lessons

perfect squares:

${\left( {x + a} \right)^2} = {x^2} + 2ax + {a^2}$
${\left( {x - a} \right)^2} = {x^2} - 2ax + {a^2}$
completing the square: adding a constant to a quadratic expression to make it a perfect square

Introduction
What is “COMPLETING THE SQUARE”?
a)
Review: expanding a perfect square.

b)
How to convert a polynomial into a perfect square

c)
How to complete the square

1.
Recognizing a Polynomial that Can Be Written as a Perfect Square
Convert the following expressions into perfect squares, if possible:
a)
${x^2} + 6x + {3^2}$ =
${x^2} - 6x + {\left( { - 3} \right)^2}$ =

b)
${x^2} + 20x + 100$ =
${x^2} - 20x + 100$ =
${x^2} - 20x - 100$ =

2.
Completing the Square
Add a constant to each quadratic expression to make it a perfect square.
a)
${x^2} + 10x + \;$ _____ =

b)
${x^2} - 2x + \;$ _____ =

c)
$2{x^2} + 12x + \;$ _____ =

d)
$- 3{x^2} + 60x + \;$ _____ =

e)
$\frac{2}{5}{x^2} - 8x + \;$ _____ =

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