Question

help with cubic functions!?

Answer 1

what the problem

Answer 2

find a cubic function that fits all four of these points

Answer 3

(0, 1), (5.5, 3.2), (9, 3), (14, 6)

Answer 4

umm i sorry i dk how to do that im really sorry

Answer 5

oh okay
thanks anyways

Answer 6

im really sorry though

Answer 7

@Hero can you help me again!? I have no idea how to do this

Answer 8

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

Use that to create a system of four equations. Then solve for a,b,c,d

Answer 9

how?

Answer 10

Plug in the points

Answer 11

oh so like plug in x and y for all of them?

Answer 12

Yes

Answer 13

it says to use a 4x4 matrix to solve for a, b, c, and d...idk how to do that either

Answer 14

That can be tricky

Answer 15

Because when you are done, you will have a 5 x 4 system, not 4 x 4

Answer 16

oh..so what do i do?

Answer 17

You'll probably have to use approximation methods

Answer 18

@SolomonZelman can you help me?

Answer 19

I'll try my best, but I doubt if hero couldn't help.

Continuing from what Hero said, do you know the approximation method?

Answer 20

...no :(

Answer 21

wait, does it make a difference if the problem says to use a 4x4 inverse matrix? or is that the same as a 4x4 matrix?

Answer 22

I am really bad at math, idk what the inverse matrix is, inverse of a matrix? maybe hero and ganeshea8 can help?

Answer 23

i'm sorry i thought he could help you

Answer 24

Yeah, I suck at math.

Answer 25

it's okay!

Answer 26

ty

Answer 27

esp function, I'll watch others do it.

Answer 28

i'm just soo confused and actually, I suck at math more than you do haha

Answer 29

he doesn't suck at math he's just not good with some things

Answer 30

use numerical method of approximation coz u have 4 points the greatest power in the fun would be (n-1)=(4-1)=3

Answer 31

well do u know lagrange interpolation polynomial ??

Answer 32

its a function if u apply aom point on it , it will give u polynomial that satisfy the hole point u give .
a gree untill now ??

Answer 33

matrix method gives below values for a, b, c, d; its tedious to find the inverse of coefficient matrix manually :-

http://www.wolframalpha.com/input/?i=solve+ {{0%2C0%2C0%2C1}%2C{5.5^3%2C5.5^2%2C5.5%2C1}%2C{9^3%2C9^2%2C9%2C1}%2C{14^3%2C14^2%2C14%2C1}}{{a}%2C+{b}%2C+{c}%2C+{d}}+%3D+{{1}%2C{3.2}%2C{3}%2C{6}}

lets see if this matches wid the results from ikram's method :)

Answer 34

ok, i assume u got it
so let the polyunomial u want be p(x)
f(x) is called lagrange interpolation polynomial
L(x) are interpolation coefficents