4 degree polynomial , quartic

also called a quartic equation

standard form

$f(x)=a{x}^4+b{x}^3+c{x}^2+dx+e$

turning point form

$f(x)=a(x-h{)}^4+k$

product form

$f(x)=a(x-x_1)(x-x_2)(x-x_3)(x-x_4)$