Can someone please explain the difference between factored form and vertex form?

Standard form:

ax^2 + bx + c

Vertex form:

a(x - u)^2 + v

Factored form:

a(x - p)(x - q)



Vertex form is great for finding the vertex of a parabola, and determining its nature. The vertex, in this form, is (u, v). This tells us also that the axis of symmetry is x = u. If a is positive, then the vertex is a minimum. If a is negative, then it's a maximum

Factored form is the best for finding roots, but the roots need to be neat for it to be worth it. In this form, the roots are x = p and x = q. Not every quadratic can be expressed in this form however. It relies on the quadratic actually having roots. Factored form is also great for rational functions. e.g:

y = (x - 1)/[x^2 + 2x - 3]

is not the best way to look at this function. However, if we convert to factored form:

y = (x - 1) / [(x - 1)(x + 3)]
y = 1 / (x + 3)

That is the a very comprehensive explanation
 

It's also inportant that you know how to graph them, let us know if you need assistance with that!

Yes, I'd like a little tutorial on that too. Thanks for your help mkshawty. It helped very much.