Advanced MathVery hardChoosing k for a tangent horizontal line
Advanced Math practice question
For which value of k does the line y = k touch the graph of y = x² − 6x + 11 at exactly one point?
- A. 2Correct
- B. 11
- C. 3
- D. −6
Answer: A. 2
The parabola's vertex is at x = 3, where y = 9 − 18 + 11 = 2. A horizontal line touches it once only at the vertex: k = 2.
Why the other answers are wrong
- B. 11
- 11 is the y-intercept; y = 11 crosses the parabola at two points (x = 0 and 6).
- C. 3
- 3 is the vertex's x-coordinate, not its y-coordinate.
- D. −6
- −6 is the coefficient of x.
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