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

1 Answer
Douglas K.
Mar 28, 2017

The range is #-oo < y <= 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 #-oo#.

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(0)^2+3#

#y = 3#

The range is #-oo < y <= 3#

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