y=x^2-2x-2 in vertex form

Answer 1

The equation is y = x² - 2x - 2

To change the expression (x² - 2x) into a perfect square trinomial add (half the x coefficient)² to each side of the expression.

 Here x coefficient = -2. So, (half the x coefficient)² = (-2/2)² = 1.

Add and subtract 1 to the expression.

y = (x² - 2x - 2 + 1 - 1)

y = (x² - 2x + 1 - 2 - 1)

y = (x² - 2x + 1 - 3)

y = (x² + 2(1)(x) + 1²) - 3

y  = (x - 1)² - 3

y  = 1(x - 1)² - 3

The vertex form of the parabola with vertex (h, k) and axis of symmetry x = h is y = a(x - h)² + k.

The vertex form of the equation of parabola is y  = 1(x + 1)² - 6 and Vertex : (h, k ) = (1, - 3).