# How do you find the domain and range of y=3x^2?

Jun 14, 2018

Domain: $\left\{x | x \in \mathbb{R}\right\}$

Range: $\left\{y | y \in \mathbb{R} , y \ge 0\right\}$

#### Explanation:

$y = 3 {x}^{2}$ is a quadratic function, all quadratic functions have a domain of all real numbers:

$\left\{x | x \in \mathbb{R}\right\}$

The $x$ and $y$ intercepts are both zero so the vertex is $\left(0 , 0\right)$

since the coefficient of ${x}^{2}$ is positive the parabola opens up and has a minimum so the range is:

$\left\{y | y \in \mathbb{R} , y \ge 0\right\}$

graph{3x^2 [-10, 10, -5, 5]}