# What is the domain and range of y =9 - x^2?

Sep 8, 2017

D: All real x
R: $y \le 9$

#### Explanation:

$y = 9 - {x}^{2}$ is an upside down parabola that has been shifted up 9 units. If it helps, you can rewrite the equation to make $y = - {x}^{2} + 9$.

The domain of any parabola is all real x, or $x \in \mathbb{R}$. This does not change when shifting the parabola.

The range of a normal parabola ($y = {x}^{2}$) is $y \ge 0$.

The range of an upside-down parabola ($y = - {x}^{2}$) is $y \le 0$.

Shifting the parabola up by 9 just increases the range from starting at 0 to starting at 9.

So the domain and range are:
D: All real x
R: $y \le 9$