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Answer :
Rounding all coefficients to one decimal place, the height of the object as a function of time (t) is h(t) = −4.9t²+ 33.4t + 46.0.
To find the quadratic regression equation for the given data, we can use the form:
h(t)=at²+bt+c
Using a quadratic regression calculator, we input the given data points:
(t = 0.5, h = 70.125)
(t = 1, h = 81.8)
(t = 1.5, h = 91.025)
(t = 2, h = 97.8)
(t = 2.5, h = 102.125)
(t = 3, h = 104)
After performing the quadratic regression, we get the following equation:
h(t) = −4.9t²+ 33.4t + 46.0. This equation models the height of the object over time after it is thrown.
Complete Question:
The table below shows the height, h, in meters, of an object that is thrown off the top of a building as a function of t, the time in seconds after it is thrown.
t 0.5 1 1.5 2 2.5 3
h 70.125 81.8 91.025 97.8 102.125 104
Using your calculator to perform 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. Round all numbers to one decimal place.
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Rewritten by : Jeany
