1.

x=0;  vertex (0, -3)

6a.

g = ± 15 

2.

x=-2;  vertex (-2, -5)

6b.

h = ± 6 

3.

x=-3;  vertex (-3, 7)

6c.

x = ± 5 

h = ± 2 

4.

hmmm… whatever happened to #4?

6d.

5a.

16

5b.

no real solution

Setup and Solve:
h = -16t² + 400  

The TRICK (argghh... no tricks!) here is to replace "h" with "zero", since we are interested in how much time, t, elapses until the hammer hits the ground (i.e. h = 0). So... instead...

Solve: 

0 = -16t² + 400  

Solution:
t = ± 5

answer: 5 seconds

N.B.  In the context of this problem, -5 is an extraneous solution... WHY??  

5c.

-13

5d.

±25

44.

± 6 

46.

± 3 

48.

± 6 

50.

c

58.

29

60.

15.91