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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?

User Hedy
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Quadratic Equation:
y=-x^2+12x-11

What is the Vertex?
Vertex Form:
y=a(x - h)^2 + k, where (h, k) is the vertex of the parabola.

y=-x^2+12x-11

y=(-x^2+12x)-11

y=-1(x^2-12x)-11

y=-1(x^2-12x+36-36)-11

y=-1(x^2-12x+36)+36-11

y=-1(x-6)^2+25
Vertex is (6,25)

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

Total Distance? (I assume x-intercepts)

y=-x^2+12x-11

y=-1(x^2-12x+11)

y=-(x-1)(x-11)
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: (−∞,∞),xRange: (−∞,25],y≤25
User Gapur Kassym
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