y = x²
The equation y = x² represents a parabolic function
The equation y = x² represents a parabolic function. Let me explain in more detail.
The equation y = x² is a quadratic equation. It represents a parabola, which is a U-shaped curve. In this equation, x represents the input or independent variable, and y represents the output or dependent variable.
To understand the shape of the parabola, we can plot some points. Let’s choose a few values for x and find their corresponding y values.
When x = -2, y = (-2)² = 4.
When x = -1, y = (-1)² = 1.
When x = 0, y = (0)² = 0.
When x = 1, y = (1)² = 1.
When x = 2, y = (2)² = 4.
Plotting these points on a graph, we can see that they form a symmetrical curve. The vertex, or the lowest point, of the parabola is at (0, 0).
The parabola opens upward because the coefficient of x² is positive (1 in this case). If the coefficient were negative, the parabola would open downward.
The shape of the parabola is determined by the equation y = x². Changing the value of x will give you different values of y, and these points will lie on the parabola.
Additionally, the graph is symmetric about the vertical line that passes through the vertex. This means that if you have a point (x, y) on the graph, the point (-x, y) will also be on the graph.
I hope this explanation helps! Let me know if you have any further questions.
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