question a rocket is shot off from a launcher. the accompanying table represents the height of the rocket at…

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.\ntime in seconds (x) height in feet (y)\n0.5 122\n1.6 364\n2.5 532\n3.1 636\n4.2 772\nanswer attempt 1 out of 2\nregression equation:\nfinal answer:

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.\ntime in seconds (x) height in feet (y)\n0.5 122\n1.6 364\n2.5 532\n3.1 636\n4.2 772\nanswer attempt 1 out of 2\nregression equation:\nfinal answer:

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)