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Completing the square rewrites ax² + bx + c as a(x − h)² + k with h = −b/(2a) and k = c − b²/(4a). The vertex is then read straight off, and the axis of symmetry is x = h.
Vertex
h = −b / (2a), k = c − b² / (4a)
Vertex form
y = a(x − h)² + k
h = 3 and k = 23 − 144/8 = 5, so y = 2(x − 3)² + 5 with a minimum at (3, 5).
Positive a opens the parabola upward so the vertex is the lowest point; negative a opens it downward so the vertex is the highest.