Still Confused?

Try reviewing these fundamentals first

- Home
- Transition Year Maths
- Quadratic Functions

Still Confused?

Try reviewing these fundamentals first

Still Confused?

Try reviewing these fundamentals first

Nope, got it.

That's the last lesson

Start now and get better maths marks!

Get Started NowStart now and get better maths marks!

Get Started NowStart now and get better maths marks!

Get Started NowStart now and get better maths marks!

Get Started Now- Intro Lesson14:51
- Lesson: 14:58
- Lesson: 25:17
- Lesson: 33:48
- Lesson: 45:10

Basic Concepts: Factoring polynomials: $ax^2 + bx + c$, Quadratic function in general form: $y = ax^2 + bx+c$, Quadratic function in vertex form: y = $a(x-p)^2 + q$, Completing the square

Related Concepts: Solving quadratic equations by completing the square, Graphing reciprocals of quadratic functions, System of quadratic-quadratic equations, Graphing quadratic inequalities in two variables

Step-by- step approach:

1. isolate X's on one side of the equation

2. factor out the__leading coefficient__ of $X^2$

3. "completing the square"

• X-side: inside the bracket, add (half of the coefficient of $X)^2$

• Y-side: add [__leading coefficient__ (half of the coefficient of $X)^2$ ]

4. clean up

• X-side: convert to perfect-square form

• Y-side: clean up the algebra

5. (optional)

If necessary, determine the vertex now by setting both sides of the equation equal to ZERO.

6. move the constant term from the Y-side to the X-side, and we have a quadratic function in vertex form!

1. isolate X's on one side of the equation

2. factor out the

3. "completing the square"

• X-side: inside the bracket, add (half of the coefficient of $X)^2$

• Y-side: add [

4. clean up

• X-side: convert to perfect-square form

• Y-side: clean up the algebra

5. (optional)

If necessary, determine the vertex now by setting both sides of the equation equal to ZERO.

6. move the constant term from the Y-side to the X-side, and we have a quadratic function in vertex form!

- IntroductionIntroduction to completing the square using the "6-step approach": $y=2x^2-12x+10$
- 1.
**Completing the square with NO COEFFICIENT in front of the $x^2$ term**

Convert a quadratic function from general form to vertex form by completing the square.

$y=x^2+3x-1$ - 2.
**Completing the square with a NEGATIVE COEFFICIENT in front of the $x^2$ term**

Convert a quadratic function from general form to vertex form by completing the square.

$y=-3x^2-60x-50$ - 3.
**Completing the square with a RATIONAL COEFFICIENT in front of the $x^2$ term**

Convert a quadratic function from general form to vertex form by completing the square.

$y= \frac{1}{2}x^2+x- \frac{5}{2}$ - 4.
**Completing the square with NO CONSTANT TERM**

Convert a quadratic function from general form to vertex form by completing the square.

$y=5x-x^2$

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