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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,

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

34.

Quadratic Functions

34.1

Introduction to quadratic functions

34.2

Transformations of quadratic functions

34.3

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

34.4

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

34.5

Completing the square

34.6

Converting from general to vertex form by completing the square

34.7

Shortcut: Vertex formula

34.8

Graphing quadratic functions: General form VS. Vertex form

34.9

Finding the quadratic functions for given parabolas

34.10

Applications of quadratic functions

We have over 2320 practice questions in ACCUPLACER Test Prep for you to master.

Get Started Now34.1

Introduction to quadratic functions

34.3

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

34.4

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

34.6

Converting from general to vertex form by completing the square

34.7

Shortcut: Vertex formula

34.9

Finding the quadratic functions for given parabolas