Exploring the Graph of the Function y = x^2 | Plotting and Analyzing the Parabolic Shape, Symmetry, and Vertex

graph of x^2

The graph of the function y = x^2 is a parabola

The graph of the function y = x^2 is a parabola.

To plot the graph, we can start by choosing a range of values for x. For example, let’s choose values from -5 to 5.
For each value of x, we can substitute it into the equation y = x^2 to find the corresponding value of y.

Let’s calculate some points:

When x = -5, y = (-5)^2 = 25
When x = -4, y = (-4)^2 = 16
When x = -3, y = (-3)^2 = 9
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
When x = 3, y = (3)^2 = 9
When x = 4, y = (4)^2 = 16
When x = 5, y = (5)^2 = 25

Now, let’s plot these points on a coordinate plane.

We have a set of points (-5, 25), (-4, 16), (-3, 9), (-2, 4), (-1, 1), (0, 0), (1, 1), (2, 4), (3, 9), (4, 16), and (5,25).

Connecting these points, we can see that the graph is in the shape of a “U” or an upside-down “U” depending on the orientation.

It is symmetrical with respect to the y-axis, as for any x value, there is a corresponding -x value with the same y value. The vertex of the parabola is at the point (0,0), which is called the origin.

As we move to the right of the vertex, the values of y increase. As we move to the left of the vertex, the values of y also increase since squaring any negative number will give a positive result.

The graph continues in both directions, going up and down indefinitely.

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