Relation Between Roots and Graph

Relation Between Roots and Graph

## Formula

For:

$$f(x)=a(x-\alpha)(x-\beta)$$

the roots are:

$$x=\alpha,\beta$$

and the vertex lies at:

$$x=\frac{\alpha+\beta}{2}$$

The axis of symmetry is:

$$x=\frac{\alpha+\beta}{2}$$

## Usage

- Used to determine the graph's symmetry directly from its roots.