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 . Using this equation, find the height, , at a time of 12.1 seconds. Time in Seconds (x) Height in Feet (y)
0.5 121
1.4 321
2.2 467
2.8 573
3.3 649

The height at time of 12.1 seconds is approximately 729.2562 feet

Step-by-step explanation:

The general form of the quadratic regression equation is y = A + Bx + Cx²

The quadratic regression formula is given as follows;

Solving using an online quadratic regression calculator, gives;

A = 2.5643259

B = 246.6374865

C = -15.41986006

Substituting gives;

y = 2.5643259 + 246.6374865·x -15.41986006·x²

When time, x = 12.1, we have;

y = 2.5643259 + 246.6374865×12.1 -15.41986006×12.1²≈ 729.2562 feet

The height at time of 12.1 seconds ≈ 729.2562 feet.

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