MathDB

Mr. Jones teaches algebra. He has a whiteboard with a pre-drawn coordinate grid that runs from

-10

10

in both the

x

and

y

coordinates. Consequently, when he illustrates the graph of a quadratic, he likes to use a quadratic with the following properties: I. The quadratic sends integers to integers. II. The quadratic has distinct integer roots both between

-10

and

10

, inclusive. III. The vertex of the quadratic has integer

x

and

y

coordinates both between

-10

and

10

, inclusive. How many quadratics are there with these properties?

Problem Statement