You can put this solution on YOUR website!
1. For ax^2 +bx+c parabola, the vertex (x,y) is such that x=-b/(2a)
for -x^2+10x-1, x=-10/(-2*(-1)) =5, y = -(5)^2+10*(5)-1=-25+50-1=24
vertex (5,24)
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there are many other ways to get the vertex
* solve for the perfect square
* Graph
* take the derivative