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The vertex is at (-3/2, 33/4)

x=-3/2

Step-by-step explanation:

y= -x^2 -3x+6

Factor out a negative from the first two terms

y = -(x^2 +3x)  +6

Complete the square

Take 3 /2  and square it  (3/2)^2  = 9/4

The - on the outside of the parentheses means we really are subtracting it so we need to add it on the outside

y = -(x^2 + 3x + 9/4) +9/4 +6

  = -(x+3/2)^2 + 9/4 +6

Get a common denominator of 4

  = -(x+3/2)^2 + 9/4 +6*4/4

y =- (x+3/2)^2 + 9/4 +24/4

y = -(x+3/2)^2 + 33/4

y = a(x-h)^2 +k  where (h,k) is the vertex

y = -(x - -3/2)^2 + 33/4

The vertex is at (-3/2, 33/4)

The axis of symmetry is at the x coordinate of the vertex

x=-3/2

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