**Quadratic equations.**
Provided ,
the solutions of a *quadratic equation*
are given by

(3) |

**Parabola.**
The graph of an equation
with leading coefficient
represents a parabola.
It opens upward if , or downward if .
The lowest point of an upward parabola is called the *vertex* of the
parabola. Likewise, the vertex of a downward parabola is the highest point.

**Quadratic functions.**
A function is called a *quadratic function* if

(4) |

with leading coefficient . The quadratic function represents a parabola; it opens upward if , or downward if . When , the graph of has -intercepts; the exact values of -intercepts are given by (3). There is no -intercept if .

**Standard equations of parabola.**
The quadratic function (4) is also written in the form

(5) |

The formula (5) is called a

Department of Mathematics