Graph of y = x²
Interactive graph of y = x² (x squared). Explore the standard parabola, its vertex, axis of symmetry, and key properties with our free graphing calculator.
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Drag to pan, scroll to zoom, click on the curve to pin coordinates. Edit equations in the sidebar.
Understanding the Function
The function y = x² is the most fundamental quadratic function and produces a U-shaped curve called a parabola. Its vertex sits at the origin (0, 0) and opens upward, meaning every output value is zero or positive. The curve is perfectly symmetric about the y-axis, so f(x) = f(-x) for all x.
This parabola is the parent function for all quadratic equations of the form y = ax² + bx + c. Transformations such as vertical stretching, horizontal shifting, and reflection all build on this basic shape. Understanding y = x² is essential for studying projectile motion, optimization problems, and the geometry of conic sections.
Key properties include: the vertex at (0, 0), the axis of symmetry along x = 0, the y-intercept at 0, and a domain of all real numbers with a range of [0, infinity). The derivative is 2x, meaning the slope increases linearly as you move away from the vertex.