Function Grapher

Draws the graph of an equation such as y = 2x + 1 on the coordinate plane and marks intercepts, local maxima and minima and intersections. Use it to check graphs of linear, quadratic or trigonometric functions, or to show them on a classroom screen.

How to use

1. Type an equation into "Expression 1", for example y = x^2 - 4. Press "Add expression" to draw another graph on the same plane.
2. Drag to move the graph, and use the wheel or two fingers to zoom. "Back to origin" and "Fit to graphs" reset the view.
3. With "Key points" on, press a round marker to see its coordinates. With "Trace" on, the values at the cursor are shown.
4. Letters such as a and b create sliders under "Letter values". For teaching, use "Large (classroom)" and "Full screen".

How it works

• Write a point as (2, 3), a vertical line as x = 2 and a region as y > x^2. Up to 12 expressions can be drawn.
• Angles are in radians. For degrees, add deg, as in sin(30 deg).
• Key points are found numerically within the range on screen, so points very close together can be missed.
• The "Table of values" lists function values for a range of x. Your equations are saved in this browser on this device, and "Copy link" creates a link that contains them.

Questions and answers

How do I find where two graphs intersect?

Enter each equation in its own box. Intersections are marked, and pressing one shows its coordinates. y = x^2 - 4 and y = x + 2 meet at (−2, 0) and (3, 5).

Can it find the vertex of a parabola?

Yes. The vertex is marked as a "Local minimum" when the parabola opens upward and as a "Local maximum" when it opens downward. The vertex of y = x^2 - 4x + 3 is (2, −1).

What happens to y = ax^2 when a changes?

Move the slider for a to see it. The larger the absolute value of a, the narrower the parabola; when a is negative, it opens downward.

Can I save the graph as an image?

Yes. "Save PNG" downloads the coordinate plane as shown on screen.