Answer:
see explanation
Step-by-step explanation:
The axis of symmetry is at the midpoint of the zeros
To find the zeros equate y to 0, that is
x² - 2x = 0 ← take out a common factor x
x(x - 2) = 0
equate each factor to zero and solve for x
x = 0
x - 2 = 0 ⇒ x = 2
x = [tex]\frac{0+2}{2}[/tex] ⇒ x = 1 ← equation of axis of symmetry
The vertex lies on the axis of symmetry with x-coordinate = 1
Substitute x = 1 into the equation for corresponding value of y
x = 1 : y = 1² - 2(1) = 1 - 2 = - 1
vertex = (1, - 1)
