Question

the following table shows the height, h(t), in meters of an object that is thorn off the top of the building, t seconds after it was thrown.

using your calculator to do a quadratic regression express the height of the object as a function of the number of seconds that have passed since the object was thrown use the indicated variables and proper function notation

Answer 1

I don’t see the table values. Please paste the t and h(t) data (or an image of the table). Once you do, I will run the quadratic regression and give you h(t) in proper function notation.

While you copy the table, here are short instructions (so you can run the regression yourself if you want) and what the final answer will look like.

1) Form you should get:
h(t) = a t^2 + b t + c (height in meters, t in seconds)

2) TI-84 / TI-83 instructions
- STAT → 1:Edit… → enter the t values in L1 and the h values in L2.
- STAT → CALC → A:QuadReg (or 5:QuadReg).
- Press ENTER. The calculator will return a, b, c.
- If you want to store it as a function: press VARS → Y-VARS → 1:Function… → Y1. Then after QuadReg, press VARS → Y-VARS → 1:Function… to put the regression into Y1.

3) Casio (many models)
- MODE → STAT → choose quadratic regression (or STAT → Reg → Quad).
- Enter pairs (t, h) and compute regression; it will return a, b, c.

4) Desmos / online
- In Desmos enter lists: e.g. t = [1,2,3], h = [5,2,-4] then enter: y1 ~ a x^2 + b x + c. Desmos will fit and show a, b, c.

5) If you don’t have a calculator
- I can compute the quadratic regression for you if you paste the data here, or I can show how to use Python/numpy.polyfit.

Paste the table and I’ll give the exact h(t) = at^2 + bt + c with coefficients rounded as you prefer.