**Jack draws a Penguin & asks Don to help
him describe it** **using the graphs of equations!**

**It took us about 4 months to finish, but we did it.
The # of the equation is circled.**

** Each equation led to a lot of discussion-
multiplying signed numbers in 1), the equation of a circle in 4), slope
and intercept for the lines 2), 3), 5), and 6),... and what the limits of the x and y values needed to
be in all of them.**

**For the top part we tried the parabola x ^{2
}= y, then ^{-}x^{2}=y to
open downward, but that was too thin. We ended with a wider parabola ^{-}(1/2)*x^{2}
=y (circled
1) with ^{-}4<=x<=4
to approximate Jack's picture. Note
^{-}8<=y reads y is
greater than or equal to ^{-}8.**

**The under-flap equations 2) and 3)
are both linear with opposite slopes: 2). is (1/2)*x-4=y
with x-limits ^{-}4<=x<=^{-}2
and 3). ^{-}(1/2)*x-4=y
with x-limits 2<=x<=4, this 4 corrects the 3
on the graph.**

**For the body we decided on parts of a circle. and discussed
the equation of a circle (left, near the bottom). We came up with equation 4). x**^{2}**
+ (y+6)**^{2}** = 2.5**^{2
}^{ }a circle with radius
2.5, and the center at (0,^{-}6) and
^{-}8<=y<=^{-}5.

**For the outside of the legs we used linear graphs with
opposite slopes: 5). y= ^{-}1x-7
and 6). y=1x-7, both with the y-limits are the same: ^{-}9<=
y <=^{-}7 and ^{-}9<=
y <=^{-}7. For the
inside of the legs 7).we used the absolute value
function |x| = y with the x-limits ^{-}1<=x<=1.
N.B. |3|=3 and |^{-}3|=3.**

**The bottom of the feet we came up with 8).
as y= ^{-}10
with the x-limits ^{-}2<=x<=2.**

**Great job, Jack!!!**