16Hit1600
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?

  1. A. 2Correct
  2. B. 11
  3. C. 3
  4. 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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