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 4.9 seconds.
HELP
Time in Seconds (x) Height in Feet (y)

0.5 103
0.9 182
1.7 318
2.4 422
2.8 475
3.3 539


Regression Equation:


Final Answer:

Answer 1

The equation will be y = -14.66x² + 211.41x + 0.96. If the time is 4.9 seconds, then the height will be 685.13 feet.

What is a quadratic equation?

The quadratic equation is given as ax² + bx + c = y. Then the degree of the equation will be 2. Then we have

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.

Time                        Height in Feet

0.5                                   103

0.9                                   182

 1.7                                   318

2.4                                   422

2.8                                   475

3.3                                   539

Then the equation will be

For x = 0.5 and y = 103. Then we have

a(0.5)² + b(0.5) + c = 103

  0.25a + 0.5b + c = 103  ...1

For x = 1.7 and y = 318. Then we have

a(1.7)² + b(1.7) + c = 318

 2.89a + 1.7b + c = 318   ...2

For x = 3.3 and y = 539. Then we have

a(3.3)² + b(3.3) + c = 539

10.89a + 3.3b + c = 539  ...3

By solving equations 1, 2, and 3, we have

a = -14.66, b = 211.41, and c = 0.96

Then the equation will be

y = -14.66x² + 211.41x + 0.96

If the time is 4.9 seconds, then the height will be

y = -14.66(4.9)² + 211.41(4.9) + 0.96

y = 685.13 feet

More about the quadratic equation link is given below.

brainly.com/question/2263981

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