Question

8. The table shows the height in feet of an arrow in relation to its distance from the archer. Use your calculator

to create models this relationship, and predict how far the arrow till travel before it hits the ground.
Distance from Archer (ft)
0
75
150
225
300
375
Height (ft)
6.55
59.80
90.55
98.80
84.50
47.50
Use your calculator to create a quadratic equation that models the arrow's height.
a.
b. Coach Deline is standing 500 feet away from the archer. Will the arrow hit him? Explain your answer.

Answer 1

Explanation:

a. To create a quadratic equation that models the arrow's height, we need to find the coefficients of the equation that best fit the data. One common method is to use a least squares regression to fit the data to a quadratic equation in the form y = ax^2 + bx + c. There are several ways to perform this regression, but one common method is to use a spreadsheet program or a graphing calculator with regression capabilities.

b. Based on the quadratic equation that models the arrow's height, we can predict the height of the arrow at any distance from the archer. If Coach Deline is 500 feet away from the archer, we can plug 500 into the equation as x and find the corresponding y value. If the y value is greater than 0, then the arrow is still in the air and has not hit the ground. If the y value is equal to 0, then the arrow has hit the ground. If the y value is less than 0, then the arrow has hit the ground and passed it. Based on this information, we can determine if the arrow will hit Coach Deline or not.