Answers needed.

Question

Consider the function g(x) = -2x^2-4x+6.

1. What is the vertex of the graph of this function? _______  

1. The maximum/minimum value is  _______ .  

The axis of symmetry is  _______  .

Answer 1

y=-2x^2 - 4x +6= -2(x^2 +2x -3) = -2(x^2 +2x + 1) +6+2 = 2(x+1)^2 +8

vertex is (-1,8) = maximum point

y=a(x-h)^2 + k where (h,k) = vertex =(-1,8)

axis of symmetry is x=-1

y' = -4x -4 =0

-4x = 4

x =-1 is the x coordinate of the maximum point and the x coordinate of the line of symmetry: x=-1

plug -1 into -2x^2 -4x +6 to get the y coordinate of the maximum point which is also the vertex

y=-2(-1)^2 -4(-1) + 6 = -2 +4 +6 =8 vertex = (-1,8)