What is the range of y= -(x-2)^2+2 ?
range? from 2 to -inf
If x=inf, then y=2
if x=2, then y=-inf
I don't see any fractions there.
yes, correct. Eyes are failing.
when x=-inf, y=-inf
if x=2, y=2
when x=inf, y=inf
range from -inf to 2
Still failing.
x=inf or -inf, y=-inf.
:-)
Goodness. Terrible. I am going to bed.
To find the range of the function y = -(x - 2)^2 + 2, we need to determine the set of possible values for y.
Step 1: Identify the vertex of the parabola
The vertex form of a parabola is given by y = a(x - h)^2 + k, where (h, k) represents the vertex. In this case, the vertex is (2, 2).
Step 2: Determine if the parabola opens upward or downward
Since the coefficient in front of the squared term is negative (-1 in -(x - 2)^2), we know that the parabola opens downwards.
Step 3: Consider the y-coordinate of the vertex
The y-coordinate of the vertex represents the highest or lowest point of the parabola. In this case, the y-coordinate is 2, which is the lowest point.
Step 4: State the range
Since the parabola opens downwards and the y-coordinate of the vertex is the lowest point, the range of the function y= -(x-2)^2+2 is (-∞, 2].
Therefore, the range of the function y = -(x - 2)^2 + 2 is (-∞, 2].