Answer:
(- ∞, 4 ]
Step-by-step explanation:
To determine the range we require the coordinates of the vertex
The vertex lies on the axis of symmetry which is positioned at the midpoint of the zeros.
To obtain the zeros, equate f(x) to zero, that is
-(x + 5)(x + 1) = 0
Equate each factor to zero and solve for x
x + 5 = 0 ⇒ x = - 5
x + 1 = 0 ⇒ x = - 1
[tex]x_{vertex}[/tex] = [tex]\frac{-5-1}{2}[/tex] = [tex]\frac{-6}{2}[/tex] = - 3
Substitute x = - 3 into f(x) for corresponding value of y
f(- 3) = - (- 3 + 5)(- 3 + 1) = - (2)(- 2) = 4
Vertex = (- 3, 4)
Since a = - 1 then vertex is a maximum, hence
range is (- ∞, 4 ]
