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You can find the x-coordinate of it's vertex by taking it's derivative and solving for zero:

y = -3x2 + 12x - 5

y' = -6x + 12

0 = -6x + 12

6x = 12

x = 2

Now that we have it's x coordinate, we can plug it back into the original equation to find it's y coordinate:

y = -3x2 + 12x - 5

y = -3(2)2 + 12(2) + 5

y = -12 + 24 + 5

y = 17

So the vertex of the parabola y = -3x2 + 12x - 5 occurs at the point (2, 17).

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