16Hit 1600
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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