Question

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

xy
0,0
1,-4
2,-26
3,-48
The coefficient a =
and d=
b=
c=

Answer 1

Answer: a = -3.25, b = -4, c = 0.5 and d = -4

Explanation:

To find the coefficient of a cubic function, we can use the values in the given table to set up a system of equations and then solve for the unknowns.

Here is the system of equations we can set up using the values in the table:

y = ax^3 + bx^2 + c*x + d

0 = 0a + 0b + 0c + d

-4 = 1a - 4b + 1c + d

-26 = 8a - 4b + 2c + d

-48 = 27a - 4b + 3c + d

We can then solve this system of equations using matrix operations or Cramer's rule.

a = -26/8 = -3.25

b = -4

c = -26-8a = -26+26.5 = 0.5

d = -48-27a-4b-3c = -48+91.75-44-30.5 = -4

Therefore, the coefficient a = -3.25, b = -4, c = 0.5 and d = -4 for the cubic function y = ax³ + bx² + cx+d

It's important to note that this method of solving a system of equations is the most common way but not the only way to get the coefficients in this case.