Interactive resource
Quadratic Equation Graphing Tool
Functions. Free interactive quadratic equation graphing tool. Drag a, b, and c to explore parabola opening, axis of symmetry, and vertex — for class and…
Overview
The graph of y = ax² + bx + c is a parabola. Interactive visualization builds intuition faster than memorizing formulas: change a parameter and instantly see how the opening, axis, and vertex move.
Explanation
y = ax² + bx + c (a ≠ 0) is a parabola.
a > 0 opens up, a < 0 opens down; larger |a| is narrower.
Axis x = −b/(2a); vertex (−b/(2a), (4ac − b²)/(4a)).
How to use
- Open the interactive tool for the quadratic function scene.
- Drag the a, b, and c sliders and watch the parabola update.
- Track the axis of symmetry x = −b/(2a) and the vertex.
- Ask “what if a becomes negative?” in class or while practicing alone.
Classroom example
Start with a = 1, b = 0, c = 0 (y = x²). Change b to shift the axis. Flip the sign of a to show opening direction and max/min behavior.
Knowledge points
FAQ
Is this quadratic graphing tool free?
Yes. It runs in the browser with no install required.
Can I see the vertex and axis of symmetry?
Yes. As parameters change, the visualization labels the vertex and axis so you can match them to the formulas.
How does this relate to vertex form?
After exploring general form, open the vertex-form tool to see the same parabola written differently.
How do I write the equation afterward?
Open the equation editor and copy y = ax² + bx + c or vertex form into notes.