Formulas & tables/Mathematics/Quadratic function/Vertex form

Vertex form

f(x)=a(x−p)2+qf(x)=a(x-p)^2+q

Result unit: — (function value)

What it describes

The form showing the vertex coordinates (p,q)(p,q) — makes it easier to graph the parabola.

Symbols

aa
coefficient
p,qp, q
vertex coordinates
xx
argument

Where it comes from

Reveals the vertex (p,q)(p,q) of the parabola — makes it easier to graph and to read off the minimum or maximum value. It is obtained by completing the square.

When to use it

Finding the extremum of a function, graph translations, sketching a parabola.

Example

State the vertex of the parabola f(x)=(x−3)2+2f(x)=(x-3)^2+2.
Substitutionp=3p=3, q=2q=2.
ResultVertex W=(3,2)W=(3,2), minimum value q=2q=2.

Related formulas

Vertex coordinates Standard form

Found this formula useful? Share it.

It's free — send it to a friend who's revising.

Teaching? Embed this formula on your site.

Free widget — paste it on your school site, blog or notes. It links to the full version.

Teaching a class or tutoring? Guide students in NexTutor →