The graph of y = a(x-p)² + q is a parabola obtained by translating y = ax² by p units in the x-axis direction and q units in the y-axis direction. Its vertex is (p, q), and its axis is x = p.
Example ①
State the vertex, axis, and general shape of the graph of y = 2(x - 3)² + 1.
Answer: Vertex (3, 1), axis x = 3, opens upward（a = 2 > 0）.
State the vertex, axis, and general shape of the graph of y = 2(x - 3)² + 1.
Answer: Vertex (3, 1), axis x = 3, opens upward（a = 2 > 0）.
Key Point
- y = a(x - p)² + q → vertex (p, q), axis x = p
- Pay attention to the sign of p（if (x - 3)², then p = +3）
Practice Problems
- State the vertex and axis of y = -3(x + 2)² - 5.
Answers and Explanations
- Answer: Vertex (-2, -5), axis x = -2.