Question

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

Answer 1

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

Standard form:
`y = ax^2 + bx +c`
for some constants `a,b,c`

Vertex form:
`y=m(x-a)^2+b`
for some constants `m, a, b`
(the vertex is at `(a,b)`)

Factored form:
`y=(ax+b)(cx+d)`
or possibly
`y=m(ax+b)(cx+d)`
for some constants `a, b, c, d` (and `m`)