Determine which model best fits the data. Then write an equation for the function that models the data.

(1,3) (2,12) (3,27) (4,48)

A.y=2x

B.y=4x^{2}

C.y=2x^{2}+1

D.y=3x^{2}

Guest Mar 6, 2017

#1**+6 **

Test the points in each option to determine which one fits the data.

Start by testing the first point, x = 1 and y = 3.

A. 3 =? 2(1)

3 ≠ 2 , so option A is out.

B. 3 =? 4(1^{2})

3 ≠ 4 , so option B is out.

C. 3 =? 2(1^{2}) + 1

3 = 3 , so option C goes to the next round.

D . 3 =? 3(1^{2})

3 = 3 , so option D goes to the next round.

Test the second point, x=2 and y = 12.

C. 12 =? 2(2^{2}) + 1

12 ≠ 9 , so option C is out.

D. 12 =? 3(2^{2})

12 = 12 , option D goes to the next round.

Option D is the only remaining choice. Quickly test the other points for D:

27 =? 3(3^{2})

27 = 27

48 =? 3(4^{2})

48 = 48

y = 3x^{2} fits all the data.

**f(x) = 3x ^{2}**

hectictar
Mar 6, 2017