Formulas & tables/Mathematics/Quadratic function/Vertex coordinates

Vertex coordinates

p=−b2a,q=−Δ4ap=-\dfrac{b}{2a},\quad q=-\dfrac{\Delta}{4a}

Result unit: — (coordinates)

What it describes

The coordinates of the vertex of a parabola.

Symbols

pp
x-coordinate of the vertex
qq
y-coordinate of the vertex
a,ba, b
coefficients
Δ\Delta
discriminant

Where it comes from

The coordinates of the vertex of a parabola. pp gives the axis of symmetry, and qq — the minimum value (for a>0a>0) or maximum value (for a<0a<0).

When to use it

Extremum of a quadratic function, range, axis of symmetry.

Example

Find the vertex of the parabola f(x)=x2−4x+3f(x)=x^2-4x+3.
Substitutiona=1a=1, b=−4b=-4, Δ=16−12=4\Delta=16-12=4.
Resultp=42=2p=\dfrac{4}{2}=2, q=−44=−1⇒W=(2,−1)q=-\dfrac{4}{4}=-1\Rightarrow W=(2,-1).

Related formulas

Vertex form Discriminant

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