MathDB

Parabola

Source:

March 18, 2011

conicsparabolaanalytic geometrygeometrygeometric transformationnumber theoryrelatively prime

Problem Statement

Suppose that a parabola has vertex

\left(\tfrac{1}{4},-\tfrac{9}{8}\right)

, and equation

y=ax^2+bx+c

, where

a>0

and

a+b+c

is an integer. The minimum possible value of

a

can be written as

\tfrac{p}{q},

where

p

and

q

are relatively prime positive integers. Find

p+q