1957 AHSME Problems/Problem 40
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[hide]Problem
If the parabola has its vertex on the -axis, then must be:
Solution 1
Note that if has its vertex on the -axis, then will have its vertex on the x-axis as well. To find the location of the vertex of the parabola, we desire to put it in vertex form, where , and is the location of the vertex. However, we know that , because the vertex is on the -axis. Thus, we know that must be the square of a linear term. Thus, , which are both irrational. Thus, our answer is .
Solution 2
We know that if a parabola is given by , then the -value of the vertex is (this fact can be proven with the quadratic formula and also derivatives). Because, in this case, , . Thus, at , the parabola should have a -value of . Therefore, we have the following equation that we can solve for :
See Also
1957 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 39 |
Followed by Problem 41 | |
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