Graphing a Quadratic Function: Understanding the Behavior and Shape of y = x^2

y = x^2

The equation y = x^2 represents a quadratic function

The equation y = x^2 represents a quadratic function. In this function, the variable x is squared, and the value of y will depend on the value of x.

To graph this equation, you can start by creating a table of values. Choose different values for x and calculate the corresponding values for y. For example, you can choose x = -2, -1, 0, 1, and 2. Plugging these values into the equation, we get:

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

Now, plot these coordinate pairs (-2, 4), (-1, 1), (0, 0), (1, 1), and (2, 4) on a graph. Connect the points smoothly, and you will see a curve in the shape of a parabola.

The vertex of the parabola can be found at the point (0, 0). This is the lowest point on the graph, also known as the minimum point.

The graph of y = x^2 is a symmetric curve with the vertex as the axis of symmetry. The curve extends indefinitely in both the positive and negative direction. As x increases or decreases, the value of y increases, but at an increasing rate due to the squaring.

This equation has no known restrictions on the values of x. It can be graphed on a Cartesian plane, allowing for any real number input.

Keep in mind that the graph of y = x^2 is just one possible representation of the equation. Understanding the behavior and shape of this quadratic function will be essential in solving related problems and applications in mathematics.

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