Graphing Quadratic Functions

Axis of Symmetry

This is the vertical line passing through the vertex that cuts the parabola into two equal halves. The equation is x = -b/2a.

Domain

All "X" values

Range

All "Y" values

End behavior

The direction in which the ends of the parabola are moving towards (upwards = + infinity; and downwards = - infinity)

Parabola

The graph of a quadratic function is a U-shaped curve called a parabola

Vertex

The highest (maximum) or lowest (minimum) point of the parabola is called the vertex, which is on the Axis of Symmetry

Maximum

The highest point on the U-shaped parabola when the graph is turned down (negative)

Minimum

The lower point on the U-shaped parabola when the graph is turned up (positive)

X-Intercept

This is the point where the parabola crosses the x-axis. Plug in y = 0 and solve for x

Y-Intercept

This is the point where the parabola crosses the y-axis. Plug in x = 0 and solve for y.

Direction of Opening

When a > 0, the parabola opens upwards When a < 0, the parabola opens downwards