16Hit1600
Advanced MathVery hardChoosing c so a parabola and a line touch

Advanced Math practice question

For which value of c does the graph of y = x² + 4x + c touch the x-axis at exactly one point?

  1. A. 4Correct
  2. B. −4
  3. C. 2
  4. D. 16

Answer: A. 4

One touch means discriminant 0: 16 − 4c = 0, c = 4. Then y = (x + 2)².

Why the other answers are wrong

B. −4
c = −4 gives discriminant 32: two crossings.
C. 2
c = 2 gives discriminant 8: two crossings.
D. 16
c = 16 gives a negative discriminant: no crossings.

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