Advanced MathVery hardTangency condition for a parabola
Advanced Math practice question
In the xy-plane, the parabola y = x² + 6x + c touches the x-axis at exactly one point. What is the value of c?
Answer: 9
One touching point means a zero discriminant: 36 − 4c = 0, so c = 9.
Common wrong answers
- If you answered 3
- 3 is the x-location's magnitude (the vertex is at x = −3); c itself is 9.
- If you answered 36
- 36 is b²; set 36 − 4c = 0 and solve for c.
- If you answered -9
- A negative c would put two crossings on the axis; tangency needs c = +9.
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