Question

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

Answer 1

The vertex (0, 0), `f(-1)=0.5` and `f(1)=0.5`. You can also calculate `f(-2)=2` and `f(2)=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=ax^2+bx+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(-2)=(-2)^2/2=2`
`f(-1)=(-1)^2/2=0.5`
`f(1)=(1)^2/2=0.5`
`f(2)=(2)^2/2=2`
graph{x^2/2 [-4, 4, -2, 4]}