Functions

[soprano]

I need help with this.

A ball is propelled upward from ground level. After 't' seconds, its height in feet is a function defined by f(t)=-16t^2+112t.
After how many seconds will it reach a height of 192 feet?

 

[masters]

I need help with this.

A ball is propelled upward from ground level. After 't' seconds, its height in feet is a function defined by f(t)=-16t^2+112t.
After how many seconds will it reach a height of 192 feet?

The coordinates at the 192 feet will be (t, f(t)) which will be (t, 192), since 192 feet is a function of time.

$\displaystyle f(t)=-16t^2+112t$

$\displaystyle 192=-16t^2+112t$

$\displaystyle 16t^2-112t+192=0$

$\displaystyle t^2-7t+12=0$

I'll leave the rest to you. There will be two times when the ball will be at 192 feet. Once going up and again coming back down.