Question

4. Mr. Downey used the function f(x) = -3x2 + 12x to model the flight of a glider. In Mr. Downey's

functions, x is the amount of time that passes in minutes and f(x) is the glider's distance from the ground in
feet. After how many seconds will the glider reach its maximum distance from the ground?

Answer 1

Answer: 120 seconds

Step-by-step explanation: In order to find the maximum value of a function, you can take the derivative of the function and equalize the result to 0.

f'(x)=(-3x^2 + 12x)'=-6x+12=0

x=2

When x is 2, the function will reach its maximum value.

f(2)=-3(2)^2 + 12.2 = -12 + 24 = 12

The maximum value (f(x)) is equal to 12 and the time passed is 2 minutes which is equal to 120 seconds.

Answer 2

After 2 seconds

Explanation:

Here is the screenshot of the parabola that formed from the quadratic equation.

As you can see the maximum point of the parabola reaches 12 feet after 2 seconds.

Also as stated in the question " After how many seconds will the glider reach its maximum distance from the ground?" We are trying to see at how many seconds the glider reaches the maximum point, not how many seconds until it lands.

Thus, the answer would be 2 seconds