Difference between revisions of "2005 AMC 12B Problems/Problem 8"
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\mathrm{(C)}\ 2 \qquad | \mathrm{(C)}\ 2 \qquad | ||
\mathrm{(D)}\ 10 \qquad | \mathrm{(D)}\ 10 \qquad | ||
| − | \mathrm{(E)}\ \text{infinitely many} | + | \mathrm{(E)}\ \text{infinitely many} |
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</math> | </math> | ||
Latest revision as of 17:23, 9 September 2020
Problem
For how many values of 
is it true that the line 
passes through the
vertex of the parabola 
?
Solution
We see that the vertex of the quadratic function is 
. The y-intercept of the line is 
. We want to find the values (if any) such that 
. Solving for , the only values that satisfy this are 
and 
, so the answer is 
See also
| 2005 AMC 12B (Problems • Answer Key • Resources) | |
| Preceded by Problem 7 |
Followed by Problem 9 |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
| All AMC 12 Problems and Solutions | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
