How do you find the unknowns for a quartic function :
f(x) =ax^4+bx^3+cx^2+dx+e
Given the table of values. Determine a,b, c, d and e.
x |y
0 0
1 0
2 1
3 3
4 6
5 10
6 15
7 21
plug in some values. After 5 steps, you will have 5 equations, which you can then solve as usual. For example, if x=3,
81a+27b+9c+3d+e = 6
and so on.
What do i do when I have the 5 equation do I use elimination or substitution to find the value of a,b,c,d,e ?
Nevermind I get it now thank you!
To find the unknowns for a quartic function, you can use the values from the given table to create a system of equations. Let's go step by step:
1. Start with the general form of the quartic function: f(x) = ax^4 + bx^3 + cx^2 + dx + e.
2. Plug in the x and y values from the table into the function to create a system of equations. For example, using the first row from the table (x=0, y=0), we have:
0 = a(0)^4 + b(0)^3 + c(0)^2 + d(0) + e
3. Repeat this process for each row in the table. Here are the equations for all the x and y values from the table:
Equation 1: 0 = e
Equation 2: 0 = a + b + c + d + e
Equation 3: 1 = 16a + 8b + 4c + 2d + e
Equation 4: 3 = 81a + 27b + 9c + 3d + e
Equation 5: 6 = 256a + 64b + 16c + 4d + e
Equation 6: 10 = 625a + 125b + 25c + 5d + e
Equation 7: 15 = 1296a + 216b + 36c + 6d + e
Equation 8: 21 = 2401a + 343b + 49c + 7d + e
4. Now you have a system of eight equations (Equation 1 to Equation 8) with five unknowns (a, b, c, d, e).
5. Use a method such as substitution or elimination to solve the system of equations and find the values of a, b, c, d, and e.
Note: Solving a system of equations with five unknowns can be time-consuming and complex. You may want to use a computer algebra system or matrix methods to solve this system efficiently.