# What is the domain and range of y= -1/2 x ^2?

May 17, 2018

Domain: $\left(- \infty , \infty\right)$

Range: $\left(- \infty , 0\right]$

#### Explanation:

A parabola where $y$ is a function of $x$ always has a domain from negative to positive infinity.

Its range depends on which direction it's facing (which is determined by the $a$ value in the quadratic equation) and what the y value of the vertex is. See the graph below.

graph{-1/2 x^2 [-10, 10, -5, 5]}