Question

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?

Answer 1

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: (−∞,∞),{x|x∈R}Range: (−∞,25],{y|y≤25}