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

##### 1 Answer

May 25, 2017

Domain:

Range:

#### Explanation:

This is a polynomial, so the domain (all possible

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

#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 themaximumvalue.

So the range is