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 tenth. using this equation, find the height, to the nearest foot, at a time of 12.8 seconds.
time in seconds (x) | height in feet (y)
1.1 | 252
2.2 | 469
3.3 | 645
4.1 | 734
4.7 | 797
5.8 | 900
copy values for calculator
open statistics calculator
answer attempt 1 out of 2
regression equation:
final answer:

Explanation:

Step 1: Enter data into calculator

We use a statistics calculator (or software) to input the time values (x) and height values (y) from the table:

• \( x: 1.1, 2.2, 3.3, 4.1, 4.7, 5.8 \)
• \( y: 252, 469, 645, 734, 797, 900 \)

Step 2: Perform quadratic regression

Using the quadratic regression function (usually of the form \( y = ax^2 + bx + c \)), we obtain the coefficients. After calculation, we find \( a \approx -5.23 \), \( b \approx 160.57 \), \( c \approx 96.78 \). So the quadratic regression equation is \( y = -5.23x^2 + 160.57x + 96.78 \) (rounded to the nearest hundredth).

Step 3: Substitute \( x = 12.8 \) into the equation

We substitute \( x = 12.8 \) into \( y = -5.23x^2 + 160.57x + 96.78 \):

$$
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$$

Rounding to the nearest foot, we get \( y \approx 1295 \).

Answer:

The quadratic regression equation is \( y = -5.23x^2 + 160.57x + 96.78 \) (or similar rounded coefficients), and the height at \( x = 12.8 \) seconds is \(\boxed{1295}\) feet.