Explore the Quadratic Function Explorer
Drag a, b and c to see the parabola, roots, vertex and discriminant change. Free, no signup, runs in your browser.
- Free to use
- No signup
- Nothing to install
- Runs in your browser
Illustration. Open the tool for the real thing.
See it in action
The Quadratic Function Explorer with sample data entered and the result showing.
What is the Quadratic Function Explorer?
Drag a, b and c to see the parabola, roots, vertex and discriminant change. It runs in your browser, so a change to a setting or a drag on an object shows up at once.
Quadratics describe the arc of a ball, the shape of satellite dishes and suspension cables, profit maximisation in business and many exam problems.
3 steps to your result
Open the tool and follow along. Nothing to install.
What you get
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.
Set the discriminant to zero.
Flip the sign of a and watch the parabola turn.
Move c and see the y-intercept move.
Used for
Pick one to see how it fits.
Math learners
Algebra, geometry, trigonometry and calculus students, teachers preparing demonstrations, and self-learners who want to see the maths move.
Try it freeTeachers
For teachers: project the Quadratic Function Explorer on the board, let students predict the result, then run it together and test this: Flip the sign of a and watch the parabola turn. For students: change one thing at a time and write down what changes.
Try it freeHow it compares
A plain look at this tool next to the usual alternative.
| This simulation | Textbook diagram | |
|---|---|---|
| Interactive | Drag, tap and change settings | Fixed picture |
| Install | Nothing to install | Not needed |
| Cost | Free to use | Depends on the book |
Questions people ask
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. The Quadratic Function Explorer is free, needs no signup or download and runs in your web browser. It is part of the Math group of AZRS simulations.
Does the Quadratic Function Explorer work on a phone or tablet?
Yes. The Quadratic Function Explorer takes touch input as well as mouse input, so you can use its 3 adjustable settings with a finger. A larger screen makes the controls and graphs easier to read.
How do I use the Quadratic Function Explorer?
1. In the Quadratic Function Explorer, use the controls to change a, b, c. The simulation reacts instantly. 2. In the Quadratic Function Explorer, pick an option such as y = x², Two roots, One root, No real roots to switch modes or load an example. 3. In the Quadratic Function Explorer, press "Copy equation" to start, reset or change what is happening. 4. Start with this experiment: Set the discriminant to zero. Drag any glowing handle, object or slider with your mouse or finger and the Quadratic Function Explorer responds in real time. 5. Change one setting at a time and watch which readout moves, then compare it with this idea: a controls the opening direction and width; c is the y-intercept.
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Try the Quadratic Function Explorer now
Drag a, b and c to see the parabola, roots, vertex and discriminant change. Free to use.
Try it free