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

1 Answer
Nov 9, 2015

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]}