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Math Prize For Girls Problems
2019 Math Prize for Girls Problems
7
7
Part of
2019 Math Prize for Girls Problems
Problems
(1)
Math Prize 2019 Problem 7
Source:
10/15/2019
Mr. Jones teaches algebra. He has a whiteboard with a pre-drawn coordinate grid that runs from
−
10
-10
−
10
to
10
10
10
in both the
x
x
x
and
y
y
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
-10
−
10
and
10
10
10
, inclusive. III. The vertex of the quadratic has integer
x
x
x
and
y
y
y
coordinates both between
−
10
-10
−
10
and
10
10
10
, inclusive. How many quadratics are there with these properties?
Math Prize for Girls