Create an equation for a cubic function in standard form

f(x) = 2x³ - 10x² - 34x + 42

Step-by-step explanation:

The standard form of a cubic equation is f(x) = ax³ + bx² + cx + d

Given conditions are:

First: Zeros of the cubic function are - 3, 1, and 7

Second: f(- 2) = 54

a(-3)³ + b(-3)² + c(-3) + d = 0 ⇔ - 27a + 9b - 3c + d = 0 ...... (1)

a + b + c + d = 0 ......... (2)

a(7)³ + b(7)² + c(7) + d = 0 ⇔ 343a + 49b + 7c + d = 0 ....... (3)

a(-2)³ + b(-2)² + c(-2) + d = 54 ⇔ - 8a + 4b - 2c + d = 54 ...... (4)

We have 4 equations with 4 unknown variables.

Use Cramer's rule to solve the system

A = = 6,480

= = 12,960

= = - 64,800

= = - 220,320

= = 272,160

a = = 2

b = = - 10

c = = - 34

d = = 42  

f(x) = 2x³ - 10x² - 34x + 42

The slope best fit isc. 1/6 mile per hour

I’m pretty sure the * means multiplication. so, if you multiply 5*1, it would equal 5. they are basically are-writing 5x1 as 5*1. so they would be… 5 10152025303540455055