Standard forms let you learn valuable information about an equation just by looking at what number was put where. There are three common forms of quadratic equations, also known as second-order polynomials.
Note that variables like a, b, and c in these descriptions will change in meaning from form to form.
Advantage: Relative mathematical simplicity, sets you up to use the quadratic formula, and easy to find the y-intercept. It is just the constant y=c.
Example: $$y=2 x^2+12 x-14$$
Advantage: Easy to find the x-intercepts. They are at x=-b and x=-c. You don’t even need the quadratic formula!
Example $$y = 2(x+7)(x-1)$$
Advantage: Easy to find the vertex, which is at (h,k).
Example: $$y=2 (x+3)^2-32$$