# Answer to Question #30771 in Algebra for arcdp

Question #30771

what is the value of N in the table?

x 0 1 2 3 4

y 0 3 12 27 N

x 0 1 2 3 4

y 0 3 12 27 N

Expert's answer

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

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

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