A hot-air balloon’s path is modeled using the function f(x)=−x2+150. A mine shaft elevator’s path is modeled using the function f(x)=−20x. Using GeoGebra, graph the two situations. Which statement correctly interprets the graphs?
The starting point of the balloons is higher than that of the elevator.
The balloon will reach the ground before the elevator does.
Negative range values don't make sense for either scenario.
Positive domain values don't make sense for either scenario.
3 answers
The starting point of the balloon is higher than that of the elevator is the correct statement to interpret the graphs.
Why?
It can be observed from the given functions that the coefficient of x in the balloon's function f(x) = -x^2 + 150 is negative and larger in magnitude than the coefficient of x in the elevator's function f(x) = -20x. This means that the rate at which the balloon is descending is faster than the rate at which the elevator is descending. Therefore, the starting point of the balloon is higher than that of the elevator.
1 answer