How do I find the equation of a cubic with the points. (50,5) (70,36) (39.3,17.5) and (81.7,24)

Answer 1

y=ax^3+bx^2+cx+d

50= 125a+25b+5c+d

36= (70^3)a + 4900b+70c+d

17.5=(39.3^3)a +(39.5^2)b +39.5c + d

24= (81.7^3)a +(81.7^2)b+81.7c+d

4 equations 4 variables

use substitution elimination or matrix algebra

a<0, d>17.5, from plotting the points