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- Quadratic Functions

Still Confused?

Try reviewing these fundamentals first.

Still Confused?

Try reviewing these fundamentals first.

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Get Started Now- Lesson: 132:01
- Lesson: 2a11:31
- Lesson: 2b5:06
- Lesson: 2c3:27
- Lesson: 2d4:23
- Lesson: 37:16

Basic concepts: Quadratic function in general form: $y = ax^2 + bx+c$, 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,

- 1.
**Applying the “vertex formula” to find the vertex**

Find the vertex for the quadratic function $y = 2{x^2} - 12x + 10$ - 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)$y = 2{x^2} - 12x + 10$b)$y = - 3{x^2} - 60x - 50$c)$y = \frac{1}{2}{x^2} + x - \frac{5}{2}$d)$y = 5x - {x^2}$ - 3.
**Deriving the Vertex Formula**

Derive the vertex formula by completing the square:

$y=ax^2+bx+c$

:

:

$(y+\frac{(b^2-4ac)}{4a})=a(x+\frac{b}{2a})$

$\therefore$ vertex: $[\frac{-b}{2a} ,\frac{-(b^2-4ac)}{4a} ]$

4.

Quadratic Functions

4.1

Characteristics of quadratic functions

4.2

Transformations of quadratic functions

4.3

Quadratic function in general form: $y = ax^2 + bx+c$

4.4

Quadratic function in vertex form: $y = a(x-p)^2 + q$

4.5

Completing the square

4.6

Converting from general to vertex form by completing the square

4.7

Shortcut: Vertex formula

4.8

Graphing parabolas for given quadratic functions

4.9

Finding the quadratic functions for given parabolas

4.10

Applications of quadratic functions

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Get Started Now4.1

Characteristics of quadratic functions

4.3

Quadratic function in general form: $y = ax^2 + bx+c$

4.4

Quadratic function in vertex form: $y = a(x-p)^2 + q$

4.6

Converting from general to vertex form by completing the square

4.7

Shortcut: Vertex formula

4.9

Finding the quadratic functions for given parabolas