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- Quadratic Functions

Still Confused?

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

5.

Quadratic Functions

5.1

Characteristics of quadratic functions

5.2

Transformations of quadratic functions

5.3

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

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 parabolas for given quadratic functions

5.9

Finding the quadratic functions for given parabolas

5.10

Applications of quadratic functions

We have over 1040 practice questions in AU Year 12 Maths for you to master.

Get Started Now5.1

Characteristics of quadratic functions

5.3

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

5.4

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

5.6

Converting from general to vertex form by completing the square

5.7

Shortcut: Vertex formula

5.9

Finding the quadratic functions for given parabolas