Graphing the equation y = x² is a fundamental skill in algebra. This equation represents a parabola, which is a U-shaped curve. Here’s a step-by-step guide to graphing y = x²:
- Understand the Equation: The equation y = x² is a quadratic function. The graph of this function is a parabola that opens upwards.
- Identify the Vertex: The vertex of the parabola is the point where the curve changes direction. For y = x², the vertex is at the origin (0, 0).
- Choose Values for x: Select a few values for x, both positive and negative. For example, you can choose x = -2, -1, 0, 1, 2.
- Calculate Corresponding y Values: Plug each x value into the equation to find the corresponding y value. For example:
- When x = -2, y = (-2)² = 4
- When x = -1, y = (-1)² = 1
- When x = 0, y = 0² = 0
- When x = 1, y = 1² = 1
- When x = 2, y = 2² = 4
- Plot the Points: On a coordinate plane, plot the points you calculated: (-2, 4), (-1, 1), (0, 0), (1, 1), (2, 4).
- Draw the Parabola: Connect the points with a smooth curve to form the parabola. Make sure the curve is symmetrical and passes through all the plotted points.
By following these steps, you can accurately graph the equation y = x². This graph is useful for understanding the behavior of quadratic functions and their applications in various fields.