2-2 The vertex form y = a(x − h)² + k

• In vertex form the vertex is (h, k) and the axis of symmetry is the line x = h.
• a > 0 the parabola opens upward and k is the minimum value; a < 0 it opens downward and k is the maximum value.
• Watch the sign inside the bracket: y = (x − 3)² + 2 has vertex (3, 2), while y = (x + 3)² − 2 has vertex (−3, −2).

Equation from the vertex and one point

• Write y = a(x − h)² + k with the given vertex, then substitute the other point to obtain a.
• Vertex (1, −4) through (3, 0): 0 = a(3 − 1)² − 4 → 4a = 4 → a = 1, so y = (x − 1)² − 4 = x² − 2x − 3.