The graph of y = x² is a parabola: a U-shape that opens upward, with its lowest point at the origin.
| Domain | All real numbers (ℝ) |
| Range | [0, ∞) |
| Symmetry | Even: symmetric about the y-axis |
| Increasing / decreasing | Decreasing on (−∞, 0], increasing on [0, ∞) |
| Key feature | Vertex (lowest point) at (0, 0) |
In y = a(x − h)² + k, the vertex moves from (0, 0) to (h, k).
a stretches the graph vertically and flips it when negative. h shifts it right (left when negative). k shifts it up (down when negative).
Can you spot a transformed x²?Play Vakra: name the curve in five plots