# What is the graph of f(x) = x^2?

Sep 13, 2014

The graph of $f \left(x\right) = {x}^{2}$ is called a "Parabola." It looks like this:

One of the ways to graph this is to use plug in a few x-values and get an idea of the shape. Since the x values keep getting squared, there is an exponential increase on either side of the y-axis. You can see this by plugging in a few values:

When
$x = 0 , f \left(x\right) = 0$
$x = 1 , f \left(x\right) = {1}^{2} = 1$
$x = 2 , f \left(x\right) = {2}^{2} = 4$
$x = 3 , f \left(x\right) = {3}^{2} = 9$
$x = 4 , f \left(x\right) = {4}^{2} = 16$

The same holds true for negative x-values to the left of the y-axis since a negative value squared is positive. For example,

$x = - 1 , f \left(x\right) = {\left(- 1\right)}^{2} = - 1 \cdot - 1 = 1$
$x = 2 , f \left(x\right) = {\left(- 2\right)}^{2} = - 2 \cdot - 2 = 4$