Find intersections, roots and turning points on a graph

Plot two or more curves and tap one: grey dots mark its roots, maximum and minimum points, y-intercept and intersections with the other curves. Tap a dot for its coordinates.

The free IB Math Revision Grapher: Where does y = x² − 2 meet y = x + 1? The grey dots mark the points of interest of the selected curve — Where does y = x² − 2 meet y = x + 1? The grey dots mark the points of interest of the selected curve. Open it in the full Grapher.

How to do it

Type the curves. One per line, for example y = x^2 - 2 and y = x + 1.
Tap a curve. Grey dots appear at its roots (x-intercepts), turning points, y-intercept and its intersections with the other curves.
Tap a dot. Its coordinates appear in a label. Values are found numerically to many significant figures; round them as the question asks.
Trace along the curve. Drag along the curve to read coordinates anywhere on it.

A parabola and a straight line in the Grapher with grey dots at their intersections, the roots and the minimum point — Selecting a curve marks its roots, turning point, y-intercept and intersections.

Good to know

To solve f(x) = g(x), graph y = f(x) and y = g(x) and read off the x-coordinates of the intersections.
Turning points are found numerically. Show the calculus in an exam answer: set dy/dx = 0 and solve.
On AA Paper 1 there is no calculator, so practise the algebra too.

Frequently asked questions

How do I find where two graphs intersect?

Type both curves, then tap one of them: grey dots mark the intersections with the other curves. Tap a dot for its coordinates.

How do I find the maximum or minimum of a function?

Tap the curve. Its turning points are marked with grey dots; tap one for its coordinates.

How accurate are the values?

They are found numerically to many more significant figures than you need. Round them as the question asks, usually 3 significant figures.

Learn more

More Grapher guides

The Grapher is our own free tool (graph.mathrevision.co.uk), built for IB, A Level and IGCSE students. It is not an exam calculator: practise on your own GDC for calculator papers.