Question

Which function's graph passes through the points (1,4), (2,9), and (3,16)?

y=5x+4
y=(x+1)^2
y=(x+3)^2
y=7x-5

Answer 1

second option is correct

Explanation:

Let equation be y =
`ax^(2) +bx+c \\`

here plugging x =1 ,x=2 and x= 15

we have

`a(1)^(2) +b(1)+c \\` = 4

a +b +c = 4 .................... equation (1)

similarly

`a(2)^(2) +b(2)+c \\`= 9

4a+2b+c = 9 ....................... equation (2)

plugging x =3 ,we get

`a(3)^(2) +b(3)+c \\` =16

9a+ 3b +c = 16 ......................... equation (3)

solving these equations simultaneously ,we have

a =1, b= 2 and c =1 ,

y=
`(1)x^(2) +2x+1\\`

y =
`(x+1)^(2) \\`

Answer 2

Put the coordinates of the points to the equations of the functions and check:

for (1, 4)

y = 5x + 4 → 4 = 5(1) + 4 → 4 = 5 + 4 → 4 = 9 FALSE

y = (x + 1)² → 4 = (1 + 1)² → 4 = 2² → 4 = 4 CORRECT

y = (x + 3)² → 4 = (1 + 3)² → 4 = 4² → 4 = 16 FALSE

y = 7x - 5 → 4 = 7(1) - 5 → 4 = 7 - 5 → 4 = 2 FALSE

Only y = (x + 1)².

Check other points:

for (2, 9)

9 = (2 + 1)² → 9 = 3² → 9 = 9 CORRECT

for (3, 16)

16 = (3 + 1)² → 16 = 4² → 16 = 16 CORRECT

Answer: Only y = (x + 1)²