Rewrite the given function into vertex form :
[tex]y=-x^2+10x-25[/tex]
Factor out the coefficient of x^2
[tex]y=-(x^2-10x+25)[/tex]
Note that the trinomial inside the parenthesis is a perfect square, this will be :
[tex]y=-(x-5)^2[/tex]
The vertex of a parabola in the form y = a(x - h)^2 + k is (h, k) and the axis of symmetry is
x = h
From the equation we have, the vertex will be at (5, 0) and the axis of symmetry is x = 5
Note that the parabola opens downward if the sign of x^2 is negative.
The graph will be :
