### Parabolas

The graph of a quadratic function is a parabola.

A
The shape of the graph of a quadratic function is a

**quadratic function**is a function, where $a$, $b$, and $c$ are real numbers and $a\neq0$, written in the form:$f(x)=ax^2+bx+c$

**parabola**. Any object thrown into the air is a projectile. When a projectile, such as a baseball, is thrown into the air at an angle, it follows a path in the shape of a parabola. So a quadratic function can be used to model the path of this type of projectile.### Properties of Parabolas

Every parabola has a vertex and an axis of symmetry.

A parabola can open upward or downward. The
If the leading coefficient is positive, then the parabola opens upward. If the leading coefficient is negative, then the parabola opens downward.
An

**vertex**is the lowest point of a parabola that opens upward or the highest point of a parabola that opens downward. The variable $a$ is the leading coefficient in a quadratic function of the form:$f(x)=ax^2+bx+c$

**axis of symmetry**is a line that divides a graph into two halves that are mirror images. For the graph of a quadratic function, the axis of symmetry is a vertical line that passes through the vertex of the parabola.