SOLUTION: Domain and range of -2x^2+3

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Question 1046278: Domain and range of -2x^2+3
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
No restriction necessary on x, so the domain is ____________________________.
(This should be obvious).

Range? Parabola concave downward, so vertex is a maximum. Easiest to see if try to solve for the zeros and check the middle value between them.
-2x%5E2%2B3=0
2x%5E2-3=0
2x%5E2=3
x%5E2=3%2F2
x=0%2B-+sqrt%283%29sqrt%282%29%2F2
x=0%2B-+sqrt%286%29%2F2
and the exact middle of these is 0. This will mean that maximum value of the expression -2x%5E2%2B3 occurs at x=0, and the range will be all values less than or equal to -2%2A0%5E2%2B3, or highlight%28y%3C=3%29.