Answer:
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
