A rock falls off a balcony. It’s height(in feet)is given by the formula f(x)= -16t^2+12.5t+150, where t is measured in seconds. How long will it take the rock to hit the ground?

Answer: [tex]3.47\ seconds[/tex]Step-by-step explanation: Given the following function: [tex]f(x)= -16t^2+12.5t+150[/tex] You need to follow these steps in order to solve the exercise: 1. Substitute [tex]f(x)=0[/tex]: [tex]0= -16t^2+12.5t+150[/tex] 2. Now you need to apply the Quadratic formula. This is: [tex]x=t=\frac{-b\±\sqrt{b^2-4ac} }{2a}[/tex] In this case, you can identify that: [tex]a=-16\\b=12.5\\c=150[/tex] Then, you can substitute these values into the formula: [tex]t=\frac{-12.5\±\sqrt{(12.5)^2-4(-16)(150)}}{2(-16)}[/tex] 3. Evaluating, you get: [tex]t_1=3.47\\\\t_2=-2.69[/tex] 4. You must choose the positive value. Then: [tex]t=3.47\ seconds[/tex]