Question

question a rocket is shot off from a launcher. the accompanying table represents the height of the rocket at given times, where x is time, in seconds, and y is height, in feet. write a quadratic regression equation for this set of data, rounding all coefficients to the nearest hundredth. using this equation, find the height, to the nearest foot, at a time of 1.6 seconds.
time in seconds (x) height in feet (y)
0.5 122
1.6 364
2.5 532
3.1 636
4.2 772
answer attempt 1 out of 2
regression equation:
final answer:

Explanation:

Step1: Use a statistics - calculator

Most scientific calculators or online statistics calculators have a quadratic regression function. Input the data points \((x,y)\) where \(x\) is the time in seconds and \(y\) is the height in feet. The general form of a quadratic regression equation is \(y = ax^{2}+bx + c\).

Step2: Obtain the coefficients

Using a statistics calculator (such as the one on a TI - 84 Plus or an online equivalent), for the data points \((0.5,122)\), \((1.6,364)\), \((2.5,532)\), \((3.1,636)\), \((4.2,772)\), we get \(a\approx - 16.00\), \(b\approx199.00\), \(c\approx24.00\). So the quadratic regression equation is \(y=-16.00x^{2}+199.00x + 24.00\).

Step3: Calculate the height at \(x = 1.6\)

Substitute \(x = 1.6\) into the equation \(y=-16.00x^{2}+199.00x + 24.00\).
\[

$$\begin{align*} y&=-16\times(1.6)^{2}+199\times1.6 + 24\\ &=-16\times2.56+318.4+24\\ &=-40.96+318.4 + 24\\ &=301.44\approx301 \end{align*}$$

\]

Answer:

Regression Equation: \(y=-16.00x^{2}+199.00x + 24.00\)
Final Answer: \(301\)