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

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

Solving the expression by completing square method we shall have:
x^2-4x+14=13
this can be written:
x^2-4x=13-14
x^2-4x=-1
but
c=(b/2a)^2
c=(-4/2*1)^2=4
thus we shall have:
x^2-4x+4=-1+4
factoring the LHS we get:
(x-2)(x-2)=3
(x-2)^2=3
getting the square root of both sides:
x-2=+/-√3
hence
x=2+/-√3
Thus the equivalent equation will be: x^2-4x+4=3