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Analyze the graph of y=-x^(2)+4x+5....

Analyze the graph of `y=-x^(2)+4x+5`.

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First observe that `a=1,b=4,c=5`. Since `a lt 0`, the parabola opens down, and the vertex is a maximum. Since `h=-(4)/(-2)=2 and k=-(2)^(2)+4(2)+5=9`, the vertex is (2,9), the maximum is 9, and the range is `(-oo, 9)`. The axis of symmetry is x=2, and the graph crosses the x-axis twice, at x=-1 and at x=5. these are the two zeros of the function and these are also the solutions to the equation `-x^(2)+4x+5=0`. the figure below shows the graph of `y=-x^(2)+4x+5`.
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