MathDB

In this question we re-define the operations addition and multiplication as follows:

a + b

is defined as the minimum of

a

and

b

, while

a * b

is defined to be the sum of

a

and

b

. For example,

3+4 = 3

3*4 = 7

, and

3*4^2+5*4+7 = \min(\text{3 plus 4 plus 4}, \text{5 plus 4}, 7) = \min(11, 9, 7) = 7.

Let

a, b, c

be real numbers. Characterize, in terms of

a, b, c

, what the graph of

y = ax^2+bx+c

looks like.

Problem Statement