Explanation:
the general equation of a parabola in a "y = ..." orientation is
y = a(x – h)² + k
where (h, k) is the vertex.
the axis of symmetry is
x = h
and for the form
y = ax²+ bx + c
this means
x = - b/(2a)
we have here
y = 3x² + 6x - 2
so we get the axis of symmetry directly :
x = -6/(2×3) = -6/6 = -1
x = -1
and we know x = h.
so we have
y = 3(x + 1)² + k = 3(x² + 2x + 1) + k =
= 3x² + 6x + 3 + k
comparing it to our original equation we see
3 + k = -2
k = -5
so, the vertex is
(-1, -5)