CorePolynomial Functions
Quadratic Function
f(x) = ax² + bx + c
Overview
A quadratic function creates a parabola. The vertex is the maximum or minimum point.
Domain
(-∞, +∞)
Range
Symmetry
Symmetric about x = -b/(2a)
Key Properties
1
Vertex at x = -b/(2a)
2
Opens up if a > 0, down if a < 0
3
Axis of symmetry: x = -b/(2a)
4
Discriminant b²-4ac determines roots
Key Insight
The vertex form f(x) = a(x-h)² + k makes it easy to read off the vertex (h, k) directly.
Visualize Quadratic Function
Interact with the graph, adjust parameters, and see how the function behaves in real time.