Find the particular equation of the cubic function that contains (-2,-35), (1,7), (2,9), and (3,25)
sheesh! What a lot of busy work.
Let y = ax^3 + bx^2 + cx + d
-8a + 4b - 2c + d = -35
a + b + c + d = 7
8a + 4b + 2c + d = 9
27a + 9b + 3c + d = 25
solve by your favorite method. Mine is wolframalpha :-)
(a,b,c,d) = (2,-5,3,7)
y = 2x^3 - 5x^2 + 3x + 7
To find the particular equation of a cubic function, we need to follow these steps:
Step 1: Set up the general equation of a cubic function
A cubic function can be represented by the equation: f(x) = ax^3 + bx^2 + cx + d
Step 2: Plug in the given points to form a system of equations
Using the given points, we can create a system of four equations, with each equation representing one of the given points. Let's substitute the x and y values of each point into the general equation:
Equation 1: -35 = a*(-2)^3 + b*(-2)^2 + c*(-2) + d
Equation 2: 7 = a*(1)^3 + b*(1)^2 + c*(1) + d
Equation 3: 9 = a*(2)^3 + b*(2)^2 + c*(2) + d
Equation 4: 25 = a*(3)^3 + b*(3)^2 + c*(3) + d
Step 3: Solve the system of equations
We now have a system of four equations with four unknowns (a, b, c, and d). We can solve this system of equations to find the values of a, b, c, and d. One way to solve it is by using a matrix calculator or numerical methods.
However, to simplify the process, we can use an online solver or a computer algebra system like Wolfram Alpha. Let's input the system of equations and solve for a, b, c, and d.
The solution to the system of equations will provide us with the values of a, b, c, and d, which we can then use to form the particular equation of the cubic function.