# What is the difference between standard form, vertex form, factored form?

May 1, 2015

Assuming that we are talking about a quadratic equation in all cases:

Standard form:
$y = a {x}^{2} + b x + c$
for some constants $a , b , c$

Vertex form:
$y = m {\left(x - a\right)}^{2} + b$
for some constants $m , a , b$
(the vertex is at $\left(a , b\right)$)

Factored form:
$y = \left(a x + b\right) \left(c x + d\right)$
or possibly
$y = m \left(a x + b\right) \left(c x + d\right)$
for some constants $a , b , c , d$ (and $m$)