diff --git a/Tests/qu2cu/qu2cu_test.py b/Tests/qu2cu/qu2cu_test.py
new file mode 100644
index 000000000..ad06448b3
--- /dev/null
+++ b/Tests/qu2cu/qu2cu_test.py
@@ -0,0 +1,83 @@
+# Copyright 2023 Behdad Esfahbod. All Rights Reserved.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+import unittest
+import pytest
+
+from fontTools.qu2cu import quadratic_to_curves, quadratics_to_curves
+
+
+class Qu2CuTest:
+    @pytest.mark.parametrize(
+        "quadratics, expected, tolerance, cubic_only",
+        [
+            (
+                [
+                    [(0, 0), (0, 1), (2, 1), (2, 0)],
+                ],
+                [
+                    ((0, 0), (0, 4 / 3), (2, 4 / 3), (2, 0)),
+                ],
+                0.1,
+                False,
+            ),
+            (
+                [
+                    [(0, 0), (0, 1), (2, 1), (2, 2)],
+                ],
+                [
+                    ((0, 0), (0, 4 / 3), (2, 2 / 3), (2, 2)),
+                ],
+                0.2,
+                False,
+            ),
+            (
+                [
+                    [(0, 0), (0, 1), (1, 1)],
+                    [(1, 1), (3, 1), (3, 0)],
+                ],
+                [
+                    ((0, 0), (0, 1), (1, 1)),
+                    ((1, 1), (3, 1), (3, 0)),
+                ],
+                0.2,
+                False,
+            ),
+            (
+                [
+                    [(0, 0), (0, 1), (1, 1)],
+                    [(1, 1), (3, 1), (3, 0)],
+                ],
+                [
+                    ((0, 0), (0, 2 / 3), (1 / 3, 1), (1, 1)),
+                    ((1, 1), (7 / 3, 1), (3, 2 / 3), (3, 0)),
+                ],
+                0.2,
+                True,
+            ),
+        ],
+    )
+    def test_simple(self, quadratics, expected, tolerance, cubic_only):
+
+        expected = [
+            tuple((pytest.approx(p[0]), pytest.approx(p[1])) for p in curve)
+            for curve in expected
+        ]
+
+        if len(quadratics) == 1:
+            c = quadratic_to_curves(quadratics[0], tolerance, cubic_only)
+            assert c == expected
+
+        c = quadratics_to_curves(quadratics, tolerance, cubic_only)
+        assert c == expected