The butterfly in this picture is going to fly down towards the flower before flying up and away. The shape it will move in is similar to a parabola. Parabola shaped graphs belong to the exponential function family.

The vertex of the graph is represented by the Flower.

The vertex of a graph is the lowest point of the graph.

Graphing Form of exponential functions:

f(x)= a (x-h) + K

A: Stretches / Condenses the graph

H: Translates parabola up / down

K: Translates parabola

Vertex: (h,k) If we move the vertex (flower) the graph also moves, this is a translation.

A,H, & K all effect different kinds of graphs the same way they do exponential graphs, but their specific graphing form may look different.

Let's look at . . .

Cubic graphs, Square root graphs, absolute value graphs, logarithmic graphs, and rational graphs.

Cubic Graph

Square Root Graph

Absolute Value Graph