Question

what is the value of N in the table?

x 0 1 2 3 4
y 0 3 12 27 N

Answer 1

at first we want to find linear function y=kx+b
x=0 then y=0, 0=k*0+b, b=0
x=1, y=3: 3=k*1then k=3
so if our function linear then y=3x but for x=2 we havey=12=3*2 so our function is not linear

suppose that function is quadratic
y=a*x^2+b*x+c
x=0, y=0 : 0=a*0+b*0+c
c=0
then y=ax^2+bx
use points x=1, y=3 and x=2, y=12
3=a*1^2+b*1 soa+b=3
12=a*2^2+b*2 so 2a+b=6
from these two equations we get a=3, b=0
then y=3x^2
we must check it on x=3, y=27:
27=3*3^2

So our function is y=3x^2
then for x=4 we get y=3*4^2=3*16=48