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You can calculate this by taking the derivative of the equation with respect to x, and solving it for a value of zero:

y = x2 - 2x - 5

∴ dy/dx = 2x - 2

Let dy/dx =0:

0 = 2x - 2

∴ 2x = 2

∴ x = 1

Now you can take that x value and plug it into the original equation to find it's y coordinate:

y = 12 - 2(1) - 5

y = 1 - 2 - 5

y = -6

So the vertex of this parabola occurs at the point (1, -6).

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Q: What is the vertex of the parabola y equals x2-2x-5?
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