Intercepts of a Quadratic

Intercepts of a Quadratic

## Formula

For:

$$y=ax^2+bx+c$$

the $y$-intercept is:

$$(0,c)$$

The $x$-intercepts are the roots:

$$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$

## Conditions / Special Cases

If:

$$D>0$$

the graph intersects the $x$-axis at two points.

If:

$$D=0$$

the graph touches the $x$-axis at one point.

If:

$$D<0$$

the graph does not intersect the $x$-axis.

## Usage

- Used to connect algebraic roots with the graphical representation of a quadratic.