Question

use the graphing tool at the right to create a scatter plot for the data in the table. use the shape of the scatter plot to determine if the data are best modeled by a linear function, an exponential function, a logarithmic function, or a quadratic function.

x	y
1	- 2
2	0
3	4
4	12

plot each point, one at a time. using the graphing tool, start by plotting (0, - 3)

Explanation:

Step1: Plot the points

Plot the points \((0, - 3)\), \((1,-2)\), \((2,0)\), \((3,4)\), \((4,12)\) on the coordinate - plane.

Step2: Analyze the shape

As \(x\) increases from \(0\) to \(4\), the differences in \(y\) - values are not constant (for linear), not growing exponentially (since the ratio of consecutive \(y\) - values is not constant), and not following a logarithmic pattern. The second - order differences of \(y\) are constant. For \(x = 0,y=-3\); \(x = 1,y=-2\) (difference in \(y\) is \(1\)); \(x = 2,y = 0\) (difference in \(y\) from previous is \(2\)); \(x = 3,y = 4\) (difference in \(y\) from previous is \(4\)); \(x = 4,y = 12\) (difference in \(y\) from previous is \(8\)). The first - order differences are \(1,2,4,8\) and the second - order differences are \(1,2,4\) which is a non - constant pattern for linear but characteristic of a quadratic function.

Answer:

The data are best modeled by a quadratic function.