Y=x²
The equation y = x² represents a parabola in the Cartesian coordinate system. It is a quadratic function with a U-shaped graph.
To understand the properties of the graph, we can look at the key components:
Vertex: The vertex of the parabola is the lowest point if the coefficient of x² is positive, or the highest point if the coefficient of x² is negative. In this case, the vertex would be at the origin (0, 0).
Symmetry: The parabola is symmetric with respect to the y-axis, meaning that if you reflect any point on the graph across the y-axis, you will get another point on the graph.
Roots: The roots (or x-intercepts) of the parabola can be found by setting y = 0 and solving for x. In this case, setting y = 0 gives us x² = 0, implying that the only root of the equation is x = 0.
Direction: Since the coefficient of x² is positive in this equation, the graph opens upwards, giving it a U-shape.
Axis of symmetry: The axis of symmetry is the vertical line that passes through the vertex. In this case, the axis of symmetry is the y-axis (x = 0).
Increasing and decreasing intervals: The graph is increasing on the intervals where x > 0 and decreasing on the intervals where x < 0.
These are some of the basic properties of the graph of y = x². Remember to use these properties to analyze and solve problems related to this equation.
