Quadratic Function Explorer
Drag a, b and c to see the parabola, roots, vertex and discriminant change.
Drag the orange vertex or the green y-intercept on the graph. The view zooms automatically so the vertex, roots and intercept never leave the screen.
About the Quadratic Function Explorer
Free interactive quadratic grapher. Change a, b and c to see the parabola, vertex, axis of symmetry, roots and discriminant update instantly. Great for algebra students. Built for math, the quadratic function explorer runs instantly in your browser: change a setting or drag an object and the result updates at once, so you learn by trying things out rather than only reading about them.
Drag a, b and c to see the parabola, roots, vertex and discriminant change. Use it to explore math ideas at your own pace, then check what you found against the key ideas further down this page.
How to use the Quadratic Function Explorer
- Use the controls to change a, b, c. The simulation reacts instantly.
- Pick an option such as y = x², Two roots, One root, No real roots to switch modes or load an example.
- Where you see a glowing handle, object, weight or atom, drag it with your mouse or finger. Everything responds in real time.
- Watch the readouts and graphs update as you experiment, and compare what you see with the key ideas below.
Things to try
- Set the discriminant to zero.
- Flip the sign of a and watch the parabola turn.
- Move c and see the y-intercept move.
- Find the vertex for x² - 4x + 1.
Key ideas you can learn
- a controls the opening direction and width; c is the y-intercept.
- The vertex is at x = -b / 2a and the axis of symmetry passes through it.
- The discriminant b² - 4ac tells you if there are two, one or no real roots.
Where this is used in the real world
Quadratics describe the arc of a ball, the shape of satellite dishes and suspension cables, profit maximisation in business and many exam problems.
Who is this simulation for?
Algebra, geometry, trigonometry and calculus students, teachers preparing demonstrations, and self-learners who want to see the maths move.
For teachers: project it on the board, let students predict what will happen, then run it together. For students: change one thing at a time and write down what changes.
Frequently asked questions
What does the discriminant tell me?
If b² - 4ac is positive there are two real roots, if zero there is one repeated root, and if negative there are no real roots (the parabola misses the x-axis).
How do I find the vertex of a parabola?
The x-coordinate is -b / 2a. Substitute it back into the equation to get the y-coordinate.
Is the Quadratic Function Explorer free to use?
Yes. It is completely free, with no signup, no download and no ads inside the simulation. It runs in your web browser.
Does the Quadratic Function Explorer work on a phone or tablet?
Yes. It uses touch as well as the mouse, so you can drag objects with your finger. A larger screen makes the controls easier to see.