The Parabolic Function F(X)=X^2: Graphing, Roots, And Symmetry

f(x)=x^2

f'(x)=2x

Function f(x)=x^2 represents a parabola. This mathematical function will give us the square of the input value x. We can graph f(x)=x^2 by plotting various input values of x on the x-axis and their corresponding output values of f(x) on the y-axis.

For example, let’s see some input-output pairs of the function f(x)=x^2:

When x=-2, f(x)=(-2)^2=4.
When x=-1, f(x)=(-1)^2=1.
When x=0, f(x)=(0)^2=0.
When x=1, f(x)=(1)^2=1.
When x=2, f(x)=(2)^2=4.

Based on the above values, we can plot the points (-2,4), (-1,1), (0,0), (1,1), (2,4) on a graph paper and draw a smooth curve through them to obtain the graph of f(x)=x^2.

The graph of the function f(x)=x^2 will always be a U-shaped curve and open upwards. This function has only one real root, which is x=0. Moreover, it is a continuous and differentiable function.

Finally, it is worth noting that since the function f(x)=x^2 is an even function, it possesses a symmetry about the y-axis.

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