The equation of a parabola has 4 general equations:
(x - h)² = 4a(y - k)
(x - h)² = -4a(y - k)
(y - k)² = 4a(x - h)
(y - k)² = 4a(x - h)
You will notice that the equation contains an x². So, our choices will be narrowed down to:
(x - h)² = 4a(y - k)
(x - h)² = -4a(y - k)
where, the vertex has the coordinates (h.k)
y = 6x² - 24x + 30
Divide both sides by 6,
y/6 = x² - 4x + 5
y/6 - 5 = x² - 4x
Completing the squares, add (-4/2)² = 4 to both sides,
y/6 - 5 + 4 = x² - 4x + 4
y/6 - 1 = (x - 2)²
1/6(y - 6) = (x - 2)²
Thus, h=2 and k=6. The vertex is at point (2,6).
