Quadratic Equations!!

Quadratic equations of one variable (unknown) appears in the form ax^2+bx+c=0 where a,b,c are constants and a≠0

Examples of quadratic equation:
Example 1: 5x^2+12x+7=0
This is a quadratic equation because a,b,c are constants and a≠0.

Example 2: 6x^2+4x=9
This is a quadratic equation because by using the Addition Property of Equality, we can change this into the form of ax^2+bx+c=0 by subtracting 2 on each side.

Example 3: 5x^2+12x=0
This is a quadratic equation because c can be 0 and a≠0.

Example 4: 6x^2-9=0
This is a quadratic equation because b can be 0 and a≠0.

For example 5, 6 and non-example 1,2
Question: Are these equations quadratic?

Example 5: (x-4)(x+2)=0
This is a quadratic equation because by using the Distributive Property, we can change this into the form of ax^2+bx+c=0 by multiplying out the terms in the brackets.

Example 6: 9x+ 5/x-11=0
This is a quadratic equation because we can change this into the form of ax^2+bx+c=0 by multiplying out the denominator.

Non-example 1: (x^2-4)(x+2)=0
This is a not a quadratic equation because by using the Distributive Property and multiplying the terms in the bracket, there is a x^3 term.

Non-example 2: 3x^2+4/x-12=0
This is a not a quadratic equation because by using the Distributive Property, there is a x^3 term.

Note: Quadratic equations always have a x^2 term, maybe a x term and a constant. The equation is also quadratic if there is a x^2 term after multiplying out.

Rationale
Recognise quadratic equations!!