Question

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

Answer 1

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

Answer 2

Answer:

second option is correct

Step-by-step 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 = $(x+1)^{2}$