im not sure how to do this question

A student fires a model rocket into the air. The rocket reaches a maximum hieght of 24.8 meters and lands 55 meters from the student. (assume parabola and no wind)

a. list three points of trajectory(coordinate pairs)

b. determine the regression equation that best fits the trajectory using your graphing calculator

I am taking a chance at this one.

See if you agree or not.

(0,0) is the initial starting point
(55, 0) is the ending point
24.8 is the max height which occurs 1/2 between 0 and 55
so that gives us another point
(27.5, 24.8)

I used the quadratic regression on the graphing calculator to get an equation.

ok thank you i will try that i have no idea how to use my calculator so i will try and do what you said.

I put the numbers in using the stat function of the TI-83.

I hit STAT and edit to put in the numbers in L1 and L2.

Then I did Stat -Calc and I chose Quadreg and L1 L2 from keyboard and enter.

yes that worked in the calulator and i had an idea that those would be the points.

using the graphing calulator how do you find the regression equation? could you walk me through it? so i can do it on the calculator ?

To answer this question, let's break it down step by step.

a. List three points of trajectory (coordinate pairs):
To find three points on the trajectory of the rocket, we need to know the height and horizontal distance at three different instances. We know the maximum height is 24.8 meters and the horizontal distance from the student is 55 meters. We can assume the rocket is launched from the origin (0,0). Now, let's find the coordinate pairs.

1. Coordinate pair at launch: (0, 0) - Since the rocket is launched from the origin, the initial height at launch is 0.

2. Coordinate pair at maximum height: (X, 24.8) - We don't know the exact value of X, so we need to find it. However, we know that the rocket reaches its maximum height when its vertical velocity becomes 0. Therefore, we can use the equation:
Initial Vertical Velocity (Uy) = 0 - Final Vertical Velocity (Vy) = ?
Using the kinematic equation:
Vy^2 = Uy^2 + 2 * g * d
where g is the acceleration due to gravity, approximately 9.8 m/s^2, and d is the vertical distance traveled.
0^2 = Uy^2 + 2 * 9.8 * d
0 = Uy^2 + 19.6 * d
Since we are looking for the maximum height, the vertical distance traveled is half the total height, so we substitute d = 12.4 into the equation:
0 = Uy^2 + 19.6 * 12.4
Uy^2 = -19.6 * 12.4
Uy = √(-19.6 * 12.4)
Therefore, the coordinate pair at the maximum height is (√(-19.6 * 12.4), 24.8).

3. Coordinate pair at landing: (55, 0) - When the rocket lands, its height is back to 0, and the horizontal distance is known to be 55 meters.

b. Determine the regression equation that best fits the trajectory using your graphing calculator:
To find the regression equation, you can use the method of least squares or a graphing calculator with regression capabilities. Follow these steps:

1. Enter the coordinate pairs obtained from the trajectory into the graphing calculator as data points.

2. Access the regression function on the calculator. The exact steps may vary depending on your calculator's brand and model. Typically, you can find it under the STAT or DATA menu.

3. Choose the regression type appropriate for a parabolic trajectory. In this case, it would be quadratic or second-degree regression.

4. Initiate the regression function and select the data points.

5. Once the regression process is complete, the calculator will display the regression equation in the form of y = Ax^2 + Bx + C. It will provide the values for A, B, and C.

That's it! You now have the regression equation that best fits the trajectory of the rocket.