# What are the important points needed to graph Y=1/2x²?

Nov 9, 2015

The vertex (0, 0), $f \left(- 1\right) = 0.5$ and $f \left(1\right) = 0.5$. You can also calculate $f \left(- 2\right) = 2$ and $f \left(2\right) = 2$.

#### Explanation:

The function $Y = {x}^{2} / 2$ is a quadratic function, therefore it has a vertex. The general rule of a quadratic function is $y = a {x}^{2} + b x + c$.
Since it doesn't have a b term, the vertex will be over the y axis. Moreover, since it doesn't have a c term, it will cross the origin. Therefore, the vertex will be located at (0, 0).
After that, just find values for y next to the vertex. At least three points are required to plot a function, but 5 are recommended.
$f \left(- 2\right) = {\left(- 2\right)}^{2} / 2 = 2$
$f \left(- 1\right) = {\left(- 1\right)}^{2} / 2 = 0.5$
$f \left(1\right) = {\left(1\right)}^{2} / 2 = 0.5$
$f \left(2\right) = {\left(2\right)}^{2} / 2 = 2$
graph{x^2/2 [-4, 4, -2, 4]}