Family of Equations

[nycmath]

Why do we call some equations linear?
Why do we call others quadratic?

A linear equation is an equation whose biggest exponent is 1.

Examples:

y = 2x, y = x + 7, y = 2x - 8

Notice that every equation has the variable x with exponent 1.

A quadratic equation is one whose biggest exponent is 2.

Examples:

y = x^2, y = x^2 + 4, y = 3x^2 - 6

What do we call the following members of the equation family?

y = x^3

y = x^4 - 3

y = x^5 + 4x

y = x^6 - 6x - 4

y = x^7

y = x^8

y = x^9 + 7x

y = x^10 - 4x^9

[Math Tutor]

They are named after the degree (the biggest exponent):

degree 3 - cubic
degree 4 - quartic
degree 5 - quintic
degree 6 - sextic

So y = x^3 is cubic, y = x^4 - 3 is quartic, y = x^5 + 4x is quintic, and so on up to y = x^10 - 4x^9, which is decic. Past degree 4 these special names are rarely used - most people just say "a polynomial of degree n".

[nycmath]

They are named after the degree (the biggest exponent):

degree 3 - cubic
degree 4 - quartic
degree 5 - quintic
degree 6 - sextic

So y = x^3 is cubic, y = x^4 - 3 is quartic, y = x^5 + 4x is quintic, and so on up to y = x^10 - 4x^9, which is decic. Past degree 4 these special names are rarely used - most people just say "a polynomial of degree n".

Thank you. This is probably the best family on earth. They don't argue or fight.

[Eigenvalue]

They are named after the degree (the biggest exponent):

degree 3 - cubic
degree 4 - quartic
degree 5 - quintic
degree 6 - sextic

So y = x^3 is cubic, y = x^4 - 3 is quartic, y = x^5 + 4x is quintic, and so on up to y = x^10 - 4x^9, which is decic. Past degree 4 these special names are rarely used - most people just say "a polynomial of degree n".

Thank you. This is probably the best family on earth. They don't argue or fight.

That is a nice joke regarding the polynomials.