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Quadratic Equations

Here are some possibilities

• Both graphs start at 42
feet above the ground, so
both times, Mario dropped
the hammer from 42 feet.
•That means that c = 42
•The blue graph starts
upward. Mario was ascending
in that mishap.
•That means the middle
coefficient is positive
•The red graph starts
decreasing immediately. The
elevator was standing still
or descending.
•If it was descending, the
middle coefficient is
•The first coefficient is -16.

What we now know:

So far, we have
h(t) = -16t2 + v0t + 42.
How can we find the value
of the initial velocity for
each graph? Let’s start
with the blue graph.
Plug the values of the
coordinates of one of the
points into the equation:

41 = -16(0.5)2 + v0 (0.5) + 42

41 = -4 + 42 + 0.5v0

3 = 0.5v0

v0 = 6

Now, you determine the equation of
the red graph

You can use either set of coordinates

h(t) = -16t2 -6t + 42

Let’s recap what we found

h(t) = -16t2 +6t + 42

Blue graph shows that Mario was
going up on the elevator at a
velocity of +6 when he dropped
hammer from a height of 42 feet.

h(t) = -16t2 -6t + 42

Red graph shows that Mario was
going down on the elevator at a
velocity of -6 when he dropped
hammer from a height of 42 feet.

What if a spider was riding on the

When Mario dropped the
hammer while he was
descending a spider went along
for the ride. How long did the
spider experience microgravity
before the hammer hit the
Ask yourself – the hammer was
how high above the ground when
it hit the ground? Plug that value
into the equation for h(t) and use
the quadratic formula to solve
for t.


How high was the hammer
above the ground when it hit
the ground?

0 feet

Plug that into the equation
For h(t).

0 = -16t2 -6t + 42

Use the quadratic
formula to solve.

X = -1.82
x = 1.44

Since this is a real world problem
We use the positive value.

The spider was “space-spider” for 1.44 seconds

** No spiders were injured in this problem

What have you learned?
Take a moment to talk with your fellow classmates about
today’s lesson:

1. How does microgravity explain why
the astronauts appear to be “floating”
inside the space shuttle?

2. What do each of the coefficients in
the quadratic equation and the vertical
motion model represent?

3. Where on the parabolic arc do the
passengers on the parabolic flight feel

4. If you know the equation of a vertical
motion problem, how can you tell how high an
object will be at .6 seconds?

Wrap it up!
We hope that you have
learned something from
Math Day 2009!

Oh, and of course. . .

We also hope that you enjoyed
the journey on the Vomit

The residents of Math Land
hope that they both
entertained you and helped you
learn about microgravity.

Your teacher has an extension
problem for you to work on.
Let us know how you solve it!