MathDB

Parabola

Source: AMC 12 2006B, Problem 12

February 17, 2006

conicsparabolaanalytic geometrycalculusalgebrasystem of equationsAMC

Problem Statement

The parabola y \equal{} ax^2 \plus{} bx \plus{} c has vertex

(p,p)

and

y

-intercept (0, \minus{} p), where

p\neq 0

. What is

b

? (A) \minus{} p \qquad (B) 0 \qquad (C) 2 \qquad (D) 4 \qquad (E) p