Relation Between Coefficients and Vertex

Relation Between Coefficients and Vertex

## Formula

For:

$$f(x)=ax^2+bx+c$$

the vertex coordinates are:

$$\left(-\frac{b}{2a},\frac{4ac-b^2}{4a}\right)$$

The $y$-intercept is:

$$f(0)=c$$

The axis of symmetry is:

$$x=-\frac{b}{2a}$$

## Usage

- Used to extract graphical information directly from the coefficients.