The
Importance
of Zeros
Lesson Five: Descartes Unit
What are we doing?
The zeros occur when the function f(x)=0. AS
with any solution, this can information can be
used to find the answers to word problems. To
demonstrate the significance of this concept, we
will begin to look over some simple word
problems that can be solved with the zeros of a
function.
*However, we will not try to solve these types of
problems yet, as they may be beyond the scope
of material we have covered.
Swimming Pool
A rectangular swimming pool is twice as long as
it is wide. A small concrete walkway surrounds
the pool. The walkway is a constant 2 feet wide
and has an area of 196 square feet. Find the
dimensions of the pool.
Answers using Zeros
Cliff Diving
Jason jumped off of a cliff
into the ocean in Acapulco
while vacationing with
some friends. His height as
a function of time could be
modeled by the function
h(t)=-16(t^2)+16t+480,
where t is the time in
seconds and h is the height
in feet. Jason hit the water
after how many seconds?
Solution using Zeros
h(t)=-16(t^2)+16t+480
0=-16(t^2)+16t+480
t=6
Rocket Launch
If a toy rocket is launched vertically upward from
ground level with an initial velocity of 128 feet
per second, then its height h after t seconds is
given by the equation h(t)=-16(t^2)+128t (if air
resistance is neglected). How long will it take for
the rocket to return to the ground?
Answer Using Zeros
h(t)=-16(t^2)+128t
0=-16(t^2)+128t
t=8 seconds
The Importance of Zeros
As you can see, the zeros of a function are the
solutions, defined when the function is equal to
zero. This information can be used in solving
various types of word problems involving
functions. We will see more of this in the coming
unit.