What is the domain and range of #y=-x^2+4x-1#?

1 Answer
May 25, 2017

Answer:

Domain: #x in RR#
Range: #y in (-oo,3]#

Explanation:

This is a polynomial, so the domain (all possible #x# values for which #y# is defined) is all real numbers, or #RR#.

To find the range, we need to find the vertex.

To find the vertex, we need to find the axis of symmetry.

The axis of symmetry is #x = -b/(2a) = -4/(2*(-1)) = 2#

Now, to find the vertex, we plug in #2# for #x# and find #y#.

#y = -(2)^2+4(2)-1#

#y = -4+8-1#

#y = 3#

The vertex is either the maximum or minimum value, depending on whether the parabola faces up or down.

For this parabola, #a = -1#, so the parabola faces down.

Therefore, #y=3# is the maximum value.

So the range is #y in (-oo,3]#