#4 · Which way does it shift?
The question. What is the vertex of the graph of y = (x − 3)² + 5?
- (−3, 5)
- (3, 5)
- (3, −5)
- (5, 3)
The shortcut. Before you pick, ask which way it shifts. The original graph, y = x², has its vertex where x is zero: (0, 0). The new graph's vertex is where x − 3 is zero, and that happens when x = 3. The + 5 lifts the whole graph 5 up. So the vertex is (3, 5). The answer is B.
Check it on the graph
If you're not sure, graph y = x² and y = (x − 3)² + 5 in the calculator built into Bluebook and look where the new vertex sits. It's at (3, 5): 3 to the right and 5 up.
The same move elsewhere
- Any function: g(x) = f(x − 4) is the graph of f moved 4 to the right.
- Circles: (x − 2)² + (y + 1)² = 9 has its center at (2, −1).
- Factors: if (x − 5) is a factor, then 5 is a zero.
The takeaway: ask which way it shifts.