1957 AMC 12 Problem 40
Attempt Problem 40 of the 1957 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1957 AMC 12 solutions, or check the answer key.
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40.
If the parabola has its vertex on the -axis, then must be:
a positive integer
a positive or a negative rational number
a positive rational number
a positive or a negative irrational number
a negative irrational number
Small hint:
A parabola whose vertex lies on the -axis has a repeated root
Big hint:
Set the discriminant of equal to zero
Solution:
The vertex lies on the -axis exactly when the quadratic has one repeated root. Its discriminant must satisfy Hence a positive or negative irrational number.
Thus, the correct answer is D.