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?
- A. 4Correct
- B. −4
- C. 2
- 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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