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Answer: ASet 6: Quadratic Equations (Advanced)
Explanation
If a parabola touches the x-axis at exactly one point, then:
A.✓ Correct
The vertex is on the x-axis
B.
The discriminant is negative
C.
It has two distinct roots
D.
It opens downward
Detailed Explanation
Choice A is correct. 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.
Key Steps:
•
The correct answer is The vertex is on the x-axis
Why others are wrong:
B: Choice B is incorrect and may result from a calculation error.
C: Choice C is incorrect and may result from a calculation error.
D: Choice D is incorrect and may result from a calculation error.
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