Vertex and Roots Relationship

Vertex and Roots Relationship

## Formula

If $$\alpha,\beta$$ are real roots, then the vertex lies midway between them:

$$x_{\text{vertex}}=\frac{\alpha+\beta}{2}$$

Therefore:

$$x_{\text{vertex}}=-\frac{b}{2a}$$

The distance from the vertex to either root is:

$$\frac{|\alpha-\beta|}{2}$$

## Usage

- Used to connect the roots, vertex and axis of symmetry.