Question

Using simultaneous equations, find a cubic model for the points (−1, −10), (2, −4), (−3, −104) and (0, −2). Show working out please.

Answer 1

set up cubic equations

Answer 2

\[c_3x^3+c_2x^2+c_1x+c_0=y\]

Answer 3

you know the x values; and y values for each one; so plug them in to set up 4 equations

Answer 4

ok got it. but after that i just solve and put all the values together to find one equation right? that's what it means by cubic model, sort of like to find the equation?

Answer 5

correct, once you do the elimination substitutions and whatever your comfortable with; you find the coeefs that define the cubic.

Answer 6

ok kool. thanks!

Answer 7

co = -2 is a good start so that eliminates alot of work

Answer 8

wait sorry, I don't how to do simultaneous equations with more than three terms properly. so once I've got D=-2 I can plug that into the equation straight away and it leaves me with the equations
-8=-A + B - C
-2= 8A + 4B + 2C
-102=-27A + 9B -3C
where would i go from there?

Answer 9

(−1, −10), (2, −4), (−3, −104) and (0, −2)

rref{{(-1)^3,(-1)^2,-1,1,-10},{(2)^3,(2)^2,2,1,-4},{(-3)^3,(-3)^2,-3,1,-104},{(0)^3,(0)^2,0,1,-2}}

http://www.wolframalpha.com/input/?i=rref%7B%7B%28-1%29%5E3%2C%28-1%29%5E2%2C-1%2C1%2C-10%7D%2C%7B%282%29%5E3%2C%282%29%5E2%2C2%2C1%2C-4%7D%2C%7B%28-3%29%5E3%2C%28-3%29%5E2%2C-3%2C1%2C-104%7D%2C%7B%280%29%5E3%2C%280%29%5E2%2C0%2C1%2C-2%7D%7D

if we use matrix methods, we get these results; which means:

y = 2x^3 -5x^2 +x -2

Answer 10

yep, i figured it out by using simultaneous equations in the end. I never learnt matrix so yeh I wouldn't understand it anyway but thanks.

Answer 11

good job :)