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: (−∞,∞),xRange: (−∞,25],y≤25