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

14.

Quadratic Functions

14.1

Characteristics of quadratic functions

14.2

Transformations of quadratic functions

14.3

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

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

We have plenty of practice questions in Transition Year Maths for you to master.

Get Started Now14.1

Characteristics of quadratic functions

14.3

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

14.4

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

14.6

Converting from general to vertex form by completing the square

14.7

Shortcut: Vertex formula

14.9

Finding the quadratic functions for given parabolas