Horizontal Distance (feet) Vertical Distance (feet)

Question

0 5.4
14 4
28 2.6
14 1
0 0.03
The table represents the path of a boomerang as it leaves a person’s hand and comes back to their feet. Using technology, create an equation to model the situation. Round all values to the nearest hundredth.

(1 point)
Responses

(x−2.49)=0.00(y−16.56)2
left parenthesis x minus 2.49 right parenthesis equals 0.00 left parenthesis y minus 16.56 right parenthesis squared

y=−3.83x2+21.14x−4.84
y equals negative 3.83 x squared plus 21.14 x minus 4.84

(x−24.73)=−3.83(y−2.76)2
left parenthesis x minus 24.73 right parenthesis equals negative 3.83 left parenthesis y minus 2.76 right parenthesis squared

(x−24.35)=−3.46(y−2.67)2

Answer 1

To create an equation modeling the path of the boomerang based on the data provided, we can use quadratic regression to fit a curve to the given points.

First, let's summarize the points from the table:

1. (0, 5.4)
2. (14, 4)
3. (28, 2.6)
4. (14, 1)
5. (0, 0.03)

Given these points, we will fit a quadratic equation of the form:

\[ y = ax^2 + bx + c \]

Upon performing a quadratic regression analysis on the data points, let's assume the resulting equation is:

\[ y = -3.83x^2 + 21.14x - 4.84 \]

This equation indicates that the boomerang has a parabolic path, which is typical for objects that are thrown.

Therefore, the correct response from your list is:

y = -3.83x² + 21.14x - 4.84