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advanced-mathIf a parabola touches the x-axis at exactly one point, then:
A
The vertex is on the x-axis
B
The discriminant is negative
C
It has two distinct roots
D
It opens downward
Correct Answer: A
Choice A is the correct answer. If a parabola touches the x-axis at only one point, that point must be the vertex (it is tangent to the axis). This corresponds to a discriminant of zero.
Choice B is incorrect because a negative discriminant means no x-intercepts. Choice C is incorrect because it has one repeated root. Choice D is incorrect because it could open upward or downward.