Hi.  I'm your teacher, Barbara Rademacher, 
and we're going to be talking about projectile 
motion.
Projectiles go up and they come down.
The first sentence of the problem gives you 
background information.  The basic equation 
is h = -16 t-squared plus v-sub-zero t plus h-
sub-zero.
Teacher reads screen.
Teacher reads screen.
Teacher reads screen.
All the numbers in those positions have 
special meanings.
So let's look at our equation
h equals -16 T squared
plus 180 T plus six.  that's called the 
trajectory. 
h is how high the ball is above the ground at 
any time
so we're going to put 206 feet in for h,
and then write down the rest of the equation.
notice it's a quadratic equation, so we have to 
use the zero principle
and subtract 206
from both sides of the equation.
that will leave us with zero equals -16 T 
squared
plus 180 T minus 200.  Teacher laughs at cat 
yeowling in background: my cat is yelling at 
me.
maybe if I pet her she'll stop making noise.
but we have to find a GCF, the greatest 
common factor
and that's going to be -4. normally I'd say four 
but if the first term as negative we have to 
make the greatest common factor negative. 
what I'm doing is I'm dividing each number by 
that GC F in order to make the numbers in the 
quadratic equation
smaller.
I'm less likely to make a mistake if I can make 
my numbers smaller.
when I divide by a negative number, all of the 
terms take on
opposite signs from what they had.
now we're going to use the quadratic formula:
our "a" will be four,  our "b" will be -45,
our "c" will be 50.
Note: you never know when my animals are 
going to chime in and help with the video so 
just be prepared.
here's the quadratic formula for T because T 
is acting like X
teacher reads the screen
teacher reads the screen
teacher reads the screen
teacher reads the screen
-teacher reads the screen
teacher reads the screen
pull the top of the radical over every number 
that's supposed to be under the radical
teacher reads the screen
teacher reads the screen
teacher reads the screen
teacher reads the screen
teacher reads the screen
teacher reads the screen
teacher reads the screen
teacher reads the screen
teacher reads the screen
teacher reads the screen
teacher reads the screen
teacher reads the screen
teacher reads the screen
teacher reads the screen
teacher reads the screen
teacher reads the screen
teacher reads the screen
teacher reads the screen
now I'm going to split T apart into two 
possible answers
45 -35 over 8
and 45 plus 35 over 8
and so T will equal10/8 which is 5/4 seconds
that time when the ball is going up
and T will equal 80/8
which is 10 seconds coming down. if you can 
imagine that a stop watch starts the instant 
the tennis player serves the ball over her 
head, that's when the ball starts going up
that's when the stop watch starts.  then, at 
1.25 seconds the ball goes through 206 ft.
the stop what keeps ticking
and the ball then again goes through 206 feet 
as it comes down
