Use cubic regression to find a function that fits the following (-3,-28) (0,-4) (4,168) (-5,-174)

f(x) = 2x³ + 3x² - x - 4

Step-by-step 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

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step-by-step explanation: