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
-	-
0	-4
1	-1
2	0
3	-1
4	-4

plot each point, one at a time. using the graphing tool, start by plotting (0, - 4).
use the graphing tool to plot (1, - 1).
use the graphing tool to plot (2, 0).
use the graphing tool to plot (3, - 1).
use the graphing tool to plot (4, - 4).

Explanation:

Step1: Plot the points

We are given the points \((0, - 4)\), \((1,-1)\), \((2,0)\), \((3,-1)\), \((4,-4)\). When we plot these points on a scatter - plot, we observe their distribution.

Step2: Analyze the shape

A linear function has points that roughly form a straight - line. An exponential function has a rapid increase or decrease. A logarithmic function has a specific curved shape related to logarithmic growth. A quadratic function has a parabolic shape.
Looking at the plotted points \((0, - 4)\), \((1,-1)\), \((2,0)\), \((3,-1)\), \((4,-4)\), we can see that the points form a parabolic shape. The data first increases from \(x = 0\) to \(x = 2\) and then decreases from \(x = 2\) to \(x = 4\).

Answer:

The data are best modeled by a quadratic function.