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f(x) = x^2 -10x - 1

What is the vertex of the parabola in a ordered pair?

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f(x)=x^2-10x-1 is the same thing as saying y=x^2-10x-1. Your first move should be to change this equation from Standard Form to Vertex Form.

Start by grouping the x^2 and x terms                                                                ------     y = (x^2-10x)-1

Next, take B (the coefficient of the x-term), divide by 2 and square the answer       -------  (-10/2)^2 = 25

Add that answer to the y and inside the parenthesis                                    -------- y+25=(x^2-10x+25)-1

Next factor and simplify to Vertex form                                                   ---------- y=(x-5)^2-26

The number inside the parenthesis is the opposite of where your vertex moves left or right and the -26 is where it moves up or down. So, your vertext would be       (5,-26)