What is the range of the function  y = -2x^2 + 3?

Mar 28, 2017

The range is $- \infty < y \le 3$

Explanation:

Please observe that the coefficient of the ${x}^{2}$ term is negative; this means that the parabola opens downward, which makes the minimum of the range approach $- \infty$.

The maximum of the range will be the y coordinate of the vertex. Because the coefficient of the $x$ term is 0, the y coordinate of vertex is the function evaluated at 0:

$y = - 2 {\left(0\right)}^{2} + 3$

$y = 3$

The range is $- \infty < y \le 3$