vertex form

Vertex form is a way of writing a quadratic that hands you the vertex for free, without any extra work. Where standard form makes you compute the turning point, vertex form simply displays it. Think of it as the parabola described by “start at this point, then open up or down by this much”.

It looks like f(x) = a(x - h)^2 + k. The pair (h, k) is the vertex itself, and a is the same leading coefficient as in standard form, controlling direction and width. Watch the sign: the form has x minus h, so f(x) = (x + 5)^2 has h = -5, not +5.

Vertex form also makes graphing transformations transparent: h shifts the basic parabola left or right, k shifts it up or down, and a stretches or flips it. You convert standard form into vertex form by completing the square, and you convert back by expanding.