red bird's flight path can be modeled by the quadratic equation y=-x^2+12x-11. What is the vertex? What is the axis of symmetry? What was the total distance? What is the domain and range?

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27-05-2016
Mathematics

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red bird's flight path can be modeled by the quadratic equation y=-x^2+12x-11. What is the vertex? What is the axis of symmetry? What was the total distance? What is the domain and range?

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Zacharias15 Zacharias15 · Answer 1 · 2016-05-28T15:51:30+02:00

Quadratic Equation: [tex]y=-x^2+12x-11[/tex]

What is the Vertex?
Vertex Form: [tex]y=a(x - h)^2 + k[/tex], where (h, k) is the vertex of the parabola.
[tex]y=-x^2+12x-11[/tex]
[tex]y=(-x^2+12x)-11[/tex]
[tex]y=-1(x^2-12x)-11[/tex]
[tex]y=-1(x^2-12x+36-36)-11[/tex]
[tex]y=-1(x^2-12x+36)+36-11[/tex]
[tex]y=-1(x-6)^2+25[/tex]
Vertex is (6,25)

Axis of Symmetry?
This is just the h value so the AoS = 6

Total Distance? (I assume x-intercepts)
[tex]y=-x^2+12x-11[/tex]
[tex]y=-1(x^2-12x+11)[/tex]
[tex]y=-(x-1)(x-11)[/tex]
x-intercepts are (1,0) and (11,0) so in between them was the flight.

Domain and Range?
I'm not sure what domain and range are but I found a calc online for it and it says
Domain: (−∞,∞),{x|x∈R}Range: (−∞,25],{y|y≤25}