Question

Find the axis of symmetry and the vertex of y=x^2-2x

Answer 1

see explanation

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 =
`(0+2)/(2)` ⇒ 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)