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2022 LMT Spring
6
2022 Spring LMT Team 6
2022 Spring LMT Team 6
Source:
September 1, 2022
algebra
Problem Statement
For all
y
y
y
, define cubic
f
y
(
x
)
f_y (x)
f
y
(
x
)
such that
f
y
(
0
)
=
y
f_y (0) = y
f
y
(
0
)
=
y
,
f
y
(
1
)
=
y
+
12
f_y (1) = y +12
f
y
(
1
)
=
y
+
12
,
f
y
(
2
)
=
3
y
2
f_y (2) = 3y^2
f
y
(
2
)
=
3
y
2
,
f
y
(
3
)
=
2
y
+
4
f_y (3) = 2y +4
f
y
(
3
)
=
2
y
+
4
. For all
y
y
y
,
f
y
(
4
)
f_y(4)
f
y
(
4
)
can be expressed in the form
a
y
2
+
b
y
+
c
ay^2 +by +c
a
y
2
+
b
y
+
c
where
a
,
b
,
c
a,b,c
a
,
b
,
c
are integers. Find
a
+
b
+
c
a +b +c
a
+
b
+
c
.
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