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Shortcut: Vertex formula
- Lesson: 132:01
- Lesson: 2a11:31
- Lesson: 2b5:06
- Lesson: 2c3:27
- Lesson: 2d4:23
- Lesson: 37:16
Shortcut: Vertex formula
Basic Concepts: Quadratic function in general form: y=ax2+bx+c, Quadratic function in vertex form: y = a(x−p)2+q, Completing the square, Converting from general to vertex form by completing the square
Related Concepts: Solving quadratic inequalities, System of linear-quadratic equations, System of quadratic-quadratic equations, Graphing quadratic inequalities in two variables
Lessons
- 1.Applying the "vertex formula" to find the vertex
Find the vertex for the quadratic function y=2x2−12x+10 - 2.Converting general form into vertex form by applying the vertex formula
Convert each quadratic function from general form to vertex form by using the vertex formula.a)y=2x2−12x+10b)y=−3x2−60x−50c)y=21x2+x−25d)y=5x−x2 - 3.Deriving the Vertex Formula
Derive the vertex formula by completing the square: y=ax2+bx+c : : (y+4a(b2−4ac))=a(x+2ab) ∴ vertex: [2a−b,4a−(b2−4ac)]
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5.
Quadratic Functions
5.1
Introduction to quadratic functions
5.2
Transformations of quadratic functions
5.3
Quadratic function in general form: y=ax2+bx+c
5.4
Quadratic function in vertex form: y = a(x−p)2+q
5.5
Completing the square
5.6
Converting from general to vertex form by completing the square
5.7
Shortcut: Vertex formula
5.8
Graphing quadratic functions: General form VS. Vertex form
5.9
Finding the quadratic functions for given parabolas
5.10
Applications of quadratic functions