how do i find equation on table?

Question

x: 1 2 3 4

y: 25 81 169 284

is this even possible?

Answer 1

284 is probably a typo and should have been 289.

a 9 can often look like a 4 if not clearly written.

then

25=5^2 for 1st term

81=9^2 for 2nd term

169=13^2 for 3rd term

289=17^2 for 4th term

441 =21^2 for 5th term

etc.

the number being squared increases by 4 each time

1+4 =5

5+4 = 9

9+4 =13

13+4 =17

17+4 = 21

it's an arithmetic sequence, before the numbers are squared

5^2, 9^2, 13^2, 17^2, 21^2, ...(4x+1)^2 , ...

y=(4x+1)^2

f(x)=(4x+1)^2

or

y= 16x^2 +8x +1

f(x)=16x^2+8x+1

or

y=16(x+1/4)^2

f(x)=16(x+1/4)^2

it's graphically an upward opening parabola

in vertex form

f(x) =16(x^2 +x/2 + 1/16) +1-1

f(x) = 16(x+1/4)^2, vertex = (-1/4,0)=minimum point

f(1)=16(5/4)^2=25

f(2)=16(9/4)^2= 81

f(3)=16(13/4)62=169

f(4)=16(17)^2=289