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y = -x2 + 1

This function describes a parabola that opens downward. To find the top of it's range, you need to find it's focal point. You can do that very easily by taking the derivative of the equation and solving it for 0:

y = -x2 + 1

∴ y' = -2x

let y' = 0:

0 = -2x

∴ x = 0

Now you can calculate the y value at that point:

y = -02 + 1

∴ y = 1

So that function describes an upside down parabola whose peak is at the point {0, 1}. It's range then is:

{y | y ∈ ℜ, y ≤ 1}

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15y ago

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Q: What is the range of the function y equals -x2 plus 1?
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