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

Apr 17, 2018

Since there are no roots or fractions, the domain is unlimited:
$- \infty < x < + \infty$

Explanation:

The smallest value of ${x}^{2}$ can be $0$ or ${x}^{2} \ge 0$

Which means that $- 2 {x}^{2} \le 0 \to - 2 {x}^{2} + 1 \le 1$

Which puts the range as: $- \infty < y \le 1$
graph{-2x^2+1 [-10, 10, -5, 5]}