1. Objective: To explore the relationship between the graphs of y = f(x) and y = f(x + k), where f(x) is in the form of ax 2 + bx + c. Prepared by Jaco Cheung & Karen Lee

2. Questions to think: (1) Are the shapes of the graphs of y = f(x) and y = f(x + k) the same? (2) How can the graph of y = f(x + k) be obtained by translating the graph of y = f(x)?

3. 0 4 c = 4 -4 -2 2 4 0 2 b = –4 -4 -2 4 a = 1 -4 -2 0 2 4 k = 0 -4 -2 0 2 y = f(x) = ax 2 + bx + c Select values of a, b & c for the graph of y = f(x)

4. 0 4 c = 4 -4 -2 2 4 0 2 b = –4 -4 -2 4 a = 1 -4 -2 0 2 4 k = 0 -4 -2 0 2 Select value of k for the new graph of y = f(x + k) y = f(x) = ax 2 + bx + c y = f(x + k)

5. 0 4 c = 4 -4 -2 2 4 0 2 b = –4 -4 -2 4 a = 1 -4 -2 0 2 4 k = 0 -4 -2 0 2 Select another value of k for the new graph of y = f(x + k) y = f(x + k) y = f(x) = ax 2 + bx + c