Step 1

We can start with the formula for the x-coordinate of the vertex of the quadratic equation: 
Where a and b are the coefficients in the general quadratic equation shown below:

Step 2

Next, to find the values of a and b, we can compare the quadratic equation with the general quadratic equation as shown:

By comparing, we have a = -3, b = -6 and c = 2

Step 3

Now, we can substitute the equation with a = -3 and b = -6. By doing so, we can solve for x.

Step 4

Hence, we have:

 x-coordinate of the vertex, x = -1

Step 5

With x = -1, we can use it to find the y-coordinate of the vertex. To do so, we substitute x = -1 into the equation as shown below:

Step 6

The y-coordinate of the vertex is 5. Therefore the coordinates of the vertex is (-1,5).

Step 7

Clearly, the answer is C.

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