MathGraph is an awesome iPad app for exploring graphs. It can be used to investigate the relationship between equations of functions and their graphs. For example, in the equation of the form , students would be able to discover that determines the appearance and steepness of the graph, while is where the graph crosses the y-axis.

MathGraph includes a variety of graphs to explore: line, circle, ellipse, parabola, hyperbola, polynomial, absolute value, exponential, logarithmic (base 10), and logarithmic (base e).

My favorite part in this app is the Quiz Me portion: the user is asked to touch the part of the graph given only the equation and the blank Cartesian plane. Shown below are sample Quiz Me questions.

- Touch the point on the graph where the line crosses the y-axis
- Touch the top of the circle
- Touch the vertex of the parabola
- Touch a point on the curve where the curve becomes horizontal

So far, this is one of the best graphing app I have explored. And the best part is, it’s FREE