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A regular-size girls' basketball was bounced from a certain height. The following data was collected and rounded to the nearest hundredth. Time (t) Height (ft) 0.01 1.88 3.05 0.11 0.21 4.13 0.31 4.91 0.41 5.37 0.51 5.50 0.61 5.31 0.71 4.82 0.81 4.00 0.91 2.97 (a) Use regression to find a quadratic model for the data. (Round the regression parameters to two decimal places.) H = Use the regression model to answer parts (b). (b) When will the ball first be 3.28 feet off the ground? (Round your answer to 3 decimal places.) seconds (c) In the box below type the equation that you need to solve in order to answer part (b).



Answer :

The quadratic model using regression for the given time(seconds) and height (feet) is given by y = 1.287x + 3.602.

Ball will be at 3.28feet when time is equal to 0.43seconds

As given in the question,

From the given time (seconds) and height(feet):

let x be the time and y be the height,

from the table consider two points get the equation of line:

( 0.01, 1.88) and (0.11 , 3.05)

(y - 1.88)/ (x - 0.01) = (3.05 - 1.88)/ (0.11- 0.01)

⇒ y= 11.7x -1.763

Using regression model calculator,

Quadratic model of the data is given by:

y = 1.287x + 3.602

When y = 3.28feet

Then 3.28 = 11.7x - 1.763

⇒x = 0.43seconds

Therefore, the quadratic model of the data using regression is given by y = 1.287x + 3.602 and ball will be at height 3.28feet when time is 0.43seconds.

Learn more about regression here

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