Answer:
A) f(x) = -16x² + 99x + 6
Step-by-step explanation:
To find the quadratic equation in the form f(x) = ax² + bx + c that models the given data, we need to use quadratic regression.
Quadratic regression is a statistical method used to find the quadratic equation that best fits a set of data points by minimizing the sum of the squares of the vertical deviations from each data point to the curve.
Input the data into a quadratic regression tool or statistical calculator, where:
- Time (seconds) is the input variable (x).
- Height (feet) is the output variable (y).
After entering the data into a statistical calculator we get:
- a = -15.7142857...
- b = 98.8571428...
- c = 5.57142857...
Round the values to the nearest whole number:
Finally, substitute the values of a, b and c into the quadratic regression formula, f(x) = ax² + bx + c:
[tex]f(x)=-16x^2+99x+6[/tex]
Therefore, the quadratic model that best represents the data is:
[tex]\Large\boxed{\boxed{f(x)=-16x^2 + 99x + 6}}[/tex]
