Answer:
vertex = (- 1, - 4.5 )
Step-by-step explanation:
Given
f(x) = [tex]\frac{1}{2}[/tex] (x - 2)(x + 4)
The vertex lies on the axis of symmetry which is positioned at the midpoint of the zeros.
To find the zeros let f(x) = 0, that is
[tex]\frac{1}{2}[/tex] (x - 2)(x + 4) = 0
Equate each factor to zero and solve for x
x - 2 = 0 ⇒ x = 2
x + 4 = 0 ⇒ x = - 4
The x- coordinate of the vertex is therefore
x = [tex]\frac{-4+2}{2}[/tex] = [tex]\frac{-2}{2}[/tex] = - 1
Substitute x = - 1 into f(x) for corresponding y- coordinate
f(- 1) = [tex]\frac{1}{2}[/tex] (- 1 - 2)(- 1 + 4) = [tex]\frac{1}{2}[/tex] × - 3 × 3 = 0.5 × - 9 = - 4.5
Coordinates of vertex = (- 1, - 4.5 )
