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- NZ Year 11 Maths
- Quadratic Functions
Completing the square
- Intro Lesson11:49
- Lesson: 1a2:25
- Lesson: 1b4:30
- Lesson: 2a1:05
- Lesson: 2b0:32
- Lesson: 2c1:49
- Lesson: 2d1:56
- Lesson: 2e3:00
Completing the square
Basic Concepts: Factoring perfect square trinomials: (a+b)2=a2+2ab+b2 or (a−b)2=a2−2ab+b2, Quadratic function in vertex form: y = a(x−p)2+q
Related Concepts: Solving quadratic equations by completing the square, Combining transformations of functions
Lessons
perfect squares:
- (x+a)2=x2+2ax+a2
- (x−a)2=x2−2ax+a2
- completing the square: adding a constant to a quadratic expression to make it a perfect square
- IntroductionWhat is "COMPLETING THE SQUARE"?
- 1.Recognizing a Polynomial that Can Be Written as a Perfect Square
Convert the following expressions into perfect squares, if possible:a)x2+6x+32 =
x2−6x+(−3)2 =b)x2+20x+100 =
x2−20x+100 =
x2−20x−100 = - 2.Completing the Square
Add a constant to each quadratic expression to make it a perfect square.a)x2+10x+_____ =b)x2−2x+_____ =c)2x2+12x+_____ =d)−3x2+60x+_____ =e)52x2−8x+_____ =
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14.
Quadratic Functions
14.1
Characteristics of quadratic functions
14.2
Transformations of quadratic functions
14.3
Quadratic function in general form: y=ax2+bx+c
14.4
Quadratic function in vertex form: y = a(x−p)2+q
14.5
Completing the square
14.6
Converting from general to vertex form by completing the square
14.7
Shortcut: Vertex formula
14.8
Graphing parabolas for given quadratic functions
14.9
Finding the quadratic functions for given parabolas
14.10
Applications of quadratic functions