Question

{(-1,9),(2,9),(5,135)} Write the equation in standard form y=ax^2+bx+c

Answer 1

So we have to fit a quadratic function?

Answer 2

yes

Answer 3

Hey Lahore.
long time no C.

Answer 4

so we have the following:
\[f(-1)=9 ; f(2)=9 ; f(5)=135\]

we need to do some plugin'

Answer 5

\[f(-1)=a-b+c=9\]
\[f(2)=4a+2b+c=9\]
\[f(5)=25a+5b+c=135\]

Answer 6

solve using gaussian elimination!!

Answer 7

1 0 0 7
0 1 0 -7
0 0 1 -5

Answer 8

a = 7, b = -7, c = 5.
or am I mistaken I will draw the graph

Answer 9

It's wrong :(

Answer 10

its alright @agd :) i kinda get it as myininaya is explaining

Answer 11

I will call numpy's quadratic fitting function and find the answer

Answer 12

my numpy implementation is broken (I'/m using a 64 bit platform so it won't work) I will code gradient descent myself!!!

Answer 13

http://en.wikipedia.org/wiki/Polynomial_regression#Matrix_form_and_calculation_of_estimates

Answer 14

thank you agdgdgdgwngo :) that is helpful .extra medal for you

Answer 15

I've found an answer.

a = 3.75
b = 0
c = 5.25

Answer 16

It doesn't fit 135 :(

Answer 17

\[a-b+c=9\]
\[4a+2b+c=9\]
\[25a+5b+c=135\]

multiply equation one by 2 and add to equation two giving us the new set of equations
\[a-b+c=9\]
\[6a+0+3c=27\]
\[25a+5b+c=135\]

multiply equation one by 5 and add to equation three giving us the new set of equations
\[a-b+c=9\]
\[6a+0+3c=27\]
\[30a+0+6c=180\]

lets simplify little before doing anything else
\[a-b+c=9\]
\[2a+0+c=9\]
\[5a+0+c=30\]

Ok multiply equation three by -1 and add to equation one and two to get the new set of equations
\[-4a-b+0=-21\]
\[-3a+0+0=-21\]
\[5a+0+c=30\]

now simplify again
\[-4a-b+0=-21\]
\[a+0+0=7\]
\[5a+0+c=30\]

Ok multiply second equation by 4 and add to equation one
\[0-b+0=7\]
\[a+0+0=7\]
\[5a+0+c=30\]

Ok multiply second equation by -5 and add to equation three
\[0-b+0=7\]
\[a+0+0=7\]
\[0+0+c=-5\]

now lets simplify alittle
\[0+b+0=-7\]
\[a+0+0=7\]
\[0+0+c=-5\]

Answer 18

wow a lot of work there myininaya :(

Answer 19

lol

Answer 20

a=7; b=-7; c=-5

Answer 21

those don't work either :(

Answer 22

i don't believe you

Answer 23

at least mine fits (1, 9) and (-1, 9)

Answer 24

let me check lol

Answer 25

wow myininaya that was awesome!!!

Answer 26

she used gauss-jordan elimination :-D

Answer 27

:D happy! thankyou so much myininaya and agdgdgdgwngo

Answer 28

wait myininaya is right!!

Answer 29

I wrote 1 instead of 2 :-P

Answer 30

i checked it
it works
lol

Answer 31

but i guess i'm late in the checking part

Answer 32

you could also just do \[\Theta = (X^TX)^{-1}*X^{T} Y\]

Answer 33

Show off!
I think this is just a algebra question?

Answer 34

man you guys are so smart:) keep it up

Answer 35

so agdgd are you going to know me what pseudoinverse means?

Answer 36

sure

Answer 37

lets go to your question