f(x) = -2 ( x+2) ^2 +1
This is written in vertex form
y = a( x-h) ^2 +k where ( h,k) is the vertex
f(x) = -2 ( x - -2)^2 +1
The vertex is (-2,1)
The axis is symmetry is along the x coordinate
The axis of symmetry is x = -2
Let x = 0 y = -2 ( 0+2) ^2 +1 = -2(2)^2 +1 = -2 *4+1 = -8+1 = -7
Let x = -1 y = -2 ( -1+2) ^2 +1 = -2(1)^2 +1 = -2 +1 = -1
Let x = -2 we know it is the vertex ( -2,1)
Let x = -3 y= -2 ( -3+2) ^2 +1 = -2(-1)^2+1 = -2(1)+1 = -2 +1 = -1
Let x = -4 y = -2 ( -4+2) ^2 +1 = -2(-2)^2+1 = -2 *4 +1 = -8+1 = -7
The domain is all real numbers since x can take any value
Since this is a downward facing parabola, it has a maximum
The range is y <= 1