Question

What is the benefit of having a quadratic on vertex form?

Answer 1

Advantages of vertex form: You can easily identify the vertex. The vertex is the point where a maximum/minimum occurs, so you'll be able to point out when, for instance, profits are maximized or costs are minimized, depending on the situation. Advantages of standard form: You can do this just as you can with vertex form, but with less work - finding roots to quadratic polynomials. Recall the quadratic formula: x=−b±b2−4ac−−−−−−−√2a are the roots to a quadratic in standard form, y=ax2+bx+c.

Answer 2

 The advantages of those forms are right in their name.
If you are trying to find the vertex of an equation, all you have to do is write down (h,k)
Standard form is good for using the quadratic formula, since it has a,b, and c
Factored form is good when trying to factor out an equation, eg (ax^2 + bx + c) and is used for writing down polynomials.