Understanding the Quadratic Function f(x) = x²: Behavior, Graph, and Symmetry

f(x)=x²

The function you have given is f(x) = x², which represents a quadratic function

The function you have given is f(x) = x², which represents a quadratic function. In this case, the variable x represents the input or independent variable, and f(x) represents the output or dependent variable.

To understand this function better, let’s look at how it behaves.

When we substitute different values for x into the function f(x) = x², we can find the corresponding values of f(x). For example:

If we substitute x = 2, then f(2) = 2² = 4.
If we substitute x = -3, then f(-3) = (-3)² = 9.

So, for any real number x, when we square it and plug it into f(x) = x², we will obtain the corresponding output value.

Graphically, the function f(x) = x² represents a parabola. The vertex of the parabola is located at the point (0, 0), and the shape of the parabola opens upward. As we move away from the vertex, the function values increase rapidly. For negative values of x, the function values are also positive due to the squaring operation.

It is worth mentioning that this function is symmetric about the y-axis since for any x, f(x) = f(-x). This means that if you were to plot points on either side of the y-axis, they would form a mirror image.

In summary, the function f(x) = x² is a quadratic function that takes any real value of x as an input and squares it to obtain the output value. It represents a symmetric parabolic curve that opens upward.

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