Advanced MathMediumCommon value at two points symmetric about a vertex
Advanced Math practice question
In the xy-plane, the graph of f(x) = (x − 4)² + 1 passes through the points (1, k) and (7, k), where k is a constant. What is the value of k?
Answer: 10
Both 1 and 7 are 3 units from the axis of symmetry x = 4, so they share a value: f(1) = 9 + 1 = 10.
Common wrong answers
- If you answered 1
- 1 is the minimum value, at x = 4.
- If you answered 9
- 9 is (1 − 4)², forgetting the +1.
- If you answered 20
- 20 adds f(1) and f(7) together; the question asks for the shared value.
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