Question

A cubic function of the form y = ax³ + bx² + cx+dyields the following table:

X Y
0 0
1 -2
2-26
3-54
The coefficient a =
and d=
b=
,C=

Answer 1

The coefficient a = -1, b = 4, c = -1 and d = 0. To solve for the coefficients, substitute the values from the table into the equation y = ax³ + bx² + cx+d. When x = 0 and y = 0, we get 0 = -1a + 4b + c + d, so d = 0. When x = 1 and y = -2, we get -2 = -1a + 4b + c, so c = -1. When x = 2 and y = -26, we get -26 = -1a + 4b, so b = 4. Finally, when x = 3 and y = -54, we get -54 = -1a, so a = -1.

Explanation: