Advanced function qestion

Question

A stunt pilot is testing a new plane. The equation that models his height over time is f(x) =15x^2 - 195x + 950 , where x is his the time in seconds and f(x) is his height in metres. Determine when the pilot is below 450 metres.

Answer 1

Set f(x) = 450, and solve the resulting quadratic equation.  Note you will have a concave-up parabola.  The time below 450 meters will be the time span from the lower to the higher root of the quadratic function.

 

15x² - 195x + 950 = 450

 

15x² - 195x + 500 = 0

 

Use the quadratic formula to find x.

 

x ≅ 3.51 or 9.49

 

The plane is below 450 meters while 3.51 < x < 9.49 seconds.