finding the domain and range of a parabola?

Question

I need to find the domain and range of y=-x^2+6x-5 and I need a lengthy description on why its the domain and range.

Answer 1

Given parabola y = -x^2+6x-5

We know that the parabola like curve .

The parabola giving us all real numbers  is the domian.

domain (-∞,∞)

To find the range

Axis of symmetry is x = -b/2a

x = -6/-2

x = 3

Substitute thex value ingiven equation.

y = -9+18-5

y = 4

Vertex of parabola is (3,4)

Vertexof parabola give us our mniimum y value thet corresponds to find the range.

Range of the parabola is y ≤ 4