State the doamin and range of y=x^2-2x+5?

Answer 1

x can be from -infinity to +infinity
y however can only be from 4 to infinity
minimum y happens when dx/dy = 0 which happens when x = 1 where y will be equal to 4

Answer 2

Another way of stating the domain of a function is thinking of it in terms of "What is x allowed to be?" In this case, this is just a parabola, or in general, a polynomial, which has no restriction for what x can't be. Therefore, the domain is all real numbers.

The proper way to solve for the range of this function is to determine the coordinates of the vertex. We need to put the function in the form

y = a(x - h)^2 + k, for a, h, k constants.

The coordinates of the vertex will be given as (h,k), and the k value will determine one of the tail ends of the range.

If "a" is positive, then we have a parabola opening upward, making the vertex (h,k) a minimum, and the range being [k,infinity). If "a" is negative, it's a parabola opening downward, and the range would be (-infinity, k].

We have to complete the square for the equation.

y = x^2 - 2x + 5

I'm going to take half of the coefficient of x (which is -2, halved is -1), and then square it ( -1 squared is +1). I'm going to add and subtract it to the equation.

y = x^2 - 2x + 1 + 5 - 1

(I inserted a +1 between the 2x and 5, and a -1 to offset the equation again.

Now, I can complete the square.

y = (x - 1)^2 + 4.

Therefore, the coordinates of the vertex is (1,4).
That would make the range [4,infinity)

Answer 3

domain is +infinty to -infinity.
range is 1 to +infinty.
reason: domain needs no contraints.
range: x^2-2x+5
=(x-2)^2+1
since the minimum value of (x-2)^2 is 0, the lower bound of y is 1. no higher bound as the value can reach infinty.