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A rocket is launched upwards from the ground. The height of the rocket above the ground is
shown in the following table:

(a) Write the quadratic regression equation that models the data. Let x = time in seconds
and let y= height in feet. Round all numbers to the nearest hundredth.
(b) Use the equation to estimate the height of rocket after 5 seconds.

A rocket is launched upwards from the ground. The height of the rocket above the ground is shown in the following table: (a) Write the quadratic regression equa class=

Answer :

raphealnwobi

The height of the rocket after 5 seconds would be 0 feet.

What is an quadratic equation?

A quadratic equation is in the form:

y = ax² + bx + c

Let y represent the height after x seconds.

At point (0, 0):

0 = a(0)² + b(0) + c

c = 0

At (0.5, 20.5):

20.5 = a(0.5)² + b(0.5) +0

0.25a + 0.5b = 20.5

At point (2, 36.25):

30.41 = a(2)² + b(2) + 0

4a + 2b = 30.41

Hence:

a = -17.2, b = 49.6

Hence:

y = -17.2x² + 49.6x

At 5 seconds:

y = -17.2(5)² + 49.6(5) = -197

The height of the rocket after 5 seconds would be 0 feet.

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