Question

What is the answer?

Answer 1

The standard eqn of a parabola in vertex form is y-k = a(x-h)^2, where (h,k) is the vertex.  There are a good number of steps involved.  I don't think it wise not to "show work."  I cannot answer this question without going through all those steps.

However, there's an easier way to find the vertex.  Identify the coefficients a, b and c:

a= -4, b= -3 and c = 1

Then the x-coord. of the vertex is x = -b / (2a).  Subst. -3 for b and -4 for a and simplify.  x = ??

Then find the y-coord. of the vertex by subbing your result, above, into the original equation. 

Write the vertex as (h,k).

Once you have this vertex, you can find the equation in vertex form as follows:

Start with the general form y-k = a(x-h)^2, where (h,k) is the vertex.

You've already found the vertex (h,k).  Subst. h and k into the general form, above.  Then only the coefficient "a" remains undefined.