Question

Based on the numbers in the table,which equation describes the value of y in terms of x

which is the right answer

A. y=x+2
B. y=3x

C. y=x^2+3

D. y =4x-1

Answer 1

Hello,

1) we imagine a linear function:
y=ax+b
(1,3)==>3=a+b (1)
(2,6)==>6=2a+b (2)
(2)-(1)==>a=3==>b=3-3=0
So we find y=3x
But (3,11)==>11=3*3 is false ==> no linear function A,B and D are false.

2) we imagine a quadratic function

y=ax²+bx+c
(1,3)==>3=a+b+c (1)
(2,6)==>6=4a+2b+c (2)
(3,11)==>11=9a+3b+c (3)

(3)-(2)==>5a+b=5 (4)
(2)-(1)==>3a+b=3 (5)

(4)-(5)==> 2a=2==> a=1
==> b=5-5*1=0
(1)==>3=1+0+c==>c=2

The quadratic function is y=x²+2
and you have make a mistake in your question!

Answer is C if you change in y=x²+2
Proof:
(4,18) 18=1*4²+0*4+2=16+2=18