19
Part of 2003 AMC 12-AHSME
Problems(2)
Parabola Transformation
Source:
2/19/2008
A parabola with equation y \equal{} ax^2 \plus{} bx \plus{} c is reflected about the -axis. The parabola and its reflection are translated horizontally five units in opposite directions to become the graphs of y \equal{} f(x) and y \equal{} g(x), respectively. Which of the following describes the graph of y \equal{} (f \plus{} g)(x)?
(A)\ \text{a parabola tangent to the }x\text{ \minus{} axis}
(B)\ \text{a parabola not tangent to the }x\text{ \minus{} axis} \qquad (C)\ \text{a horizontal line}
(D)\ \text{a non \minus{} horizontal line} \qquad (E)\ \text{the graph of a cubic function}
conicsparabolafunctiongeometrygeometric transformationreflectionanalytic geometry
Random Permutation
Source:
1/5/2009
Let be the set of permutations of the sequence for which the first term is not . A permutation is chosen randomly from . The probability that the second term is , in lowest terms, is . What is a \plus{} b?
probability