Determine if the following data set follows a linear, quadratic, or exponential model.
(−2, 10), (−1,1), (0, −2), (1,1), (2,10)
a. Linear
b. Exponential
c. Quadratic
a. Too little information to tell
looks quadratic ... y = a x^2 + bx + c
-2 = (a * 0^2) + (b * 0) + c ... c = -2
10 = 4 a + 2 b - 2 ... 4 = 2 a + b
1 = a + b - 2 ... -1 = a + b
subtracting equations ... 5 = a
... substituting ... -6 = b
y = 5 x^2 - 6 x - 2
nope ... Too little information to tell
Since the points are symmetric around (0,-2), I'd guess
y = ax^2 - 2
Using one of the points, it looks like
y = 3x^2 - 2
To determine if the given data set follows a linear, quadratic, or exponential model, we need to analyze the pattern of the data points.
First, let's plot the data points on a graph:
(-2, 10), (-1, 1), (0, -2), (1, 1), (2, 10)
From the plot, it is clear that the data set does not follow a linear or exponential model.
To determine if it follows a quadratic model, we can calculate the difference between consecutive y-values:
Difference between consecutive y-values: 10, -3, -3, 3
The differences are not constant, which indicates that the data set does not follow a quadratic model either.
Therefore, we can conclude that there is not enough information to determine the model for this data set. The answer is (d) Too little information to tell.
To determine if the given data set follows a linear, quadratic, or exponential model, we need to analyze the pattern in the data points.
One way to determine the model is by plotting the data points on a graph and observing the trend. Let's plot the data points on a coordinate plane:
(-2, 10), (-1, 1), (0, -2), (1, 1), (2, 10)
Based on the graph, it is difficult to determine the exact model. However, we can make some observations:
1. Linear model: In a linear model, the data points would fall on a straight line. Looking at the graph, the data points do not form a straight line, so we can rule out the linear model.
2. Quadratic model: In a quadratic model, the data points would form a parabolic curve. Observing the graph, the data points also do not form a parabolic curve, so we can rule out the quadratic model.
3. Exponential model: In an exponential model, the data points would show exponential growth or decay. Looking at the graph, the data points do not exhibit exponential growth or decay.
Based on the observations, we do not have enough information to determine the exact model. Therefore, the correct answer is (d) Too little information to tell.