Question

Find a quadratic model for the set of values: (-2, -20), (0, -4), (4, -20). Show your work. please help!

Answer 1

well, we can go a few different ways on this

Answer 2

the easiest please!

Answer 3

oh there is no 'easiest'

there is logical, there is systematic, there is matrix .... there is no easiest

Answer 4

please just explain a way to solve this.

Answer 5

logical

set up coefficients such that for every x value, the rest of them zero out

y = a + b(x+2) +cx(x+2)

now when x=-2, y=-20

-20 = a + b(-2+2) +c(-2)(-2+2)

b and c goto 0 leaving us

-20 = a
------------------------

next, let x=0, y=-4

-4 = a + b(0+2) +c(0)(0+2)

c goto 0 leaving us

-4 = -20 +2b, b=16/2 = 8
-------------------------

now let x = 4, y=-20; and c is the only thing left to determine

-20 = -20 + 8(4+2) +c(4)(4+2)

Answer 6

systematicly

we know ax^2 +bx +c = y gives us a quadratic; setup a system of 3 equation and the 3 unknowns can be determined

(-2)^2 a + (-2) b + c = -20
( 0)^2 a + ( 0) b + c = - 4
( 4)^2 a + ( 4) b + c = -20

c = -4 by default and this reduces to a 2 system setup

4a -2b = -20-4
16a +4b = -20-4

Answer 7

-20+4 that is

Answer 8

matrix is just to take the coeffs of the system .. and row reduce it to echelon form (rref)