(a)
the equation of a quadratic in vertex form is
y = a(x - h)² + k
where (h, k ) are the coordinates of the vertex and a is a multiplier
here the vertex = (6, - 2 ) and a = 1
y = (x - 6 )² - 2 ← in vertex form
(b)
to find the zeros let y = 0
(x - 6 )² - 2 = 0 ( add 2 to both sides )
(x - 6 )² = 2 ( take the square root of both sides )
x - 6 = ±√2 ← ( note plus or minus )
add 6 to both sides
x = 6 ±√2 ← zeros
(c)
to obtain standard form expand the vertex form of the equation
y = x² - 12x + 36 - 2
y = x² - 12x + 34 ← in standard form