Interactive resource
Parabola Vertex Form Graphing Tool
Functions. Interactive vertex-form parabola tool. Adjust a, h, and k to see how translations move the vertex.
Overview
Vertex form y = a(x − h)² + k shows the vertex (h, k) directly. Compare the base y = ax² curve with the translated graph to see shifts clearly.
Explanation
Vertex form y = a(x − h)² + k shows the vertex (h, k) directly.
From y = ax²: shift horizontally by h (h > 0 to the right), then vertically by k (k > 0 up).
Opening still depends only on a; translation does not change it.
How to use
- Open the vertex-form scene.
- Adjust h and k to move the vertex.
- Adjust a for opening direction and width.
- Use the dashed base curve to see the translation path.
Worked idea
Start from y = x², shift right by 2 (h = 2) and up by 3 (k = 3) to land on vertex (2, 3).
Knowledge points
FAQ
Vertex form vs standard form?
Standard form highlights coefficients a, b, c. Vertex form exposes the vertex for translations and max/min.
Is this tool free?
Yes. It runs in the browser with no install.
Good for class demos?
Yes — project it and ask what changes when you drag a parameter.
How do I write the formula afterward?
Open the equation editor or symbol sheet and copy a clean expression.