find range y=-x(2)-2x+3?

Question

what is the range of y=-x^2-2x+3

Answer 1

Write this expression as -x²-2x-1+1+3, -(x²+2x+1)+4, -(x+1)²+4.

So y=4-(x+1)². The squared term can’t be negative so its minimum value is zero, taken away from 4 makes the maximum value of y=4. The upper limit of y is 4. But there is no lower limit, so the range of y is (-∞,4].

Answer 2

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