SOLUTION: what is the range of the function y=-x^2 + 1

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Question 1150038: what is the range of the function y=-x^2 + 1

Found 2 solutions by Boreal, Theo:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
The vertex is at x=0 and therefore y=1
for every x, the -x^2 will be negative
therefore, the function will go to - infinity on both sides of the axis of symmetry at x=0. The largest value is 1
range is (-oo, 1]
graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C-x%5E2%2B1%29

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
the range is all values of y such that y <= 1.
since the coefficient of the x^2 term is negative, the parabola has its vertex as a maximum value and the tails point downward.
the vertex is at y = 1.
the graph of this equation is shown below.

$$$

the vertex is the highest point of the graph of the equation and ia at the point (0,1).

the tails extend forever in a negative direction.

the range is y = (-infinity,1] in interval notation.