Answer:
f(x) = 2x³ + 3x² - x - 4
Explanation:
cubic regression: f(x) = ax³ + bx² + cx + d
(0, -4) indicates that the y-intercept is -4, so
f(x) = ax³ + bx² + cx - 4
(-3, -28): f(-3) = -27a + 9b - 3c - 4 = -28
⇒ -27a + 9b - 3c = -24
(4, 168): f(4) = 64a + 16b + 4c - 4 = 168
⇒ 64a + 16b + 4c = 172
(-5, -174): f(-5) = -125a + 25b - 5c - 4 = -174
⇒ -125a + 25b - 5c = 170
Solve the 3 equations simultaneously to find a, b and c:
a = 2, b = 3, c = -1
Therefore, f(x) = 2x³ + 3x² - x - 4