A timer is started and a few moments later a swimmer dives into the water and then comes back up. The swimmer's depth (in feet) as a function of time (in seconds after the timer was started) is given by the equation h(t)=t2−12t+27
Rewrite the formula in factored form and select each true statement below.
The swimmer comes back up 9 seconds after the timer was started.
The swimmer dives into the water 12 seconds after the timer was started.
The swimmer dives into the water 3 seconds after the timer was started.
The swimmer dives to a maximum depth of 27 feet.
The swimmer is underwater for 12 seconds.
h(t) = t^2 - 12t + 27
Factored form
h(t) = (t - 9) (t - 3)
Look at the graph here (in x rather than t) : https://www.desmos.com/calculator/gug8sulzit
We can interpret this graph as follows
At t = 0 sec, the diver is 27 feet above the water
At t = 3 sec, the diver hits the water
At t = 6 sec, the diver is 9 ft below the surface
At = 9 sec, the diver returns to the surface
True statements
The swimmer comes back up 9 seconds after the timer was started.
The swimmer dives into the water 3 seconds after the timer was started.