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Brums [2.3K]
3 years ago
7

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?
Mathematics
1 answer:
Rasek [7]3 years ago
5 0
Quadratic Equation: y=-x^2+12x-11

What is the Vertex?
Vertex Form: y=a(x - h)^2 + k, where (h, k<span>) is the vertex of the parabola. 
</span>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
<span>Vertex is (6,25)

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

Total Distance? (I assume x-intercepts)
</span>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: <span><span>(<span><span>−∞</span>,∞</span>)</span>,<span>{<span>x|x∈R</span>}</span></span>Range: <span><span>(<span><span>−∞</span>,25</span>]</span>,<span>{<span>y|y≤25</span>}</span></span>
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