#### Quadratic equation in vertex form

## What is the vertex on a graph?

The vertex of a parabola is the point where the parabola crosses its axis of symmetry. If the coefficient of the x2 term is negative, the vertex will be the highest point on the graph, the point at the top of the “ U ”-shape.

## What is the equation of a parabola?

Given the focus (h,k) and the directrix y=mx+b, the equation for a parabola is (y – mx – b)^2 / (m^2 +1) = (x – h)^2 + (y – k)^2.

## What does a equal in vertex form?

Completing the Square: Finding the Vertex. y = a(x – h)^{2} + k, where (h, k) is the vertex. in y = ax^{2} + bx + c (that is, both a’s have exactly the same value). The sign on “a” tells you whether the quadratic opens up or opens down.

## Is a single vertex a graph?

1 Answer. A connected graph is a graph for which there exists a path from one vertex to any distinct vertex. Since the graph containing only a single vertex has no distinct vertices it is vacuously true that the graph containing only a single vertex is connected.