Answer:
1) The vertex form of 
is 
, 2) The stone reaches its maximum height 2 seconds after being thrown.
Step-by-step explanation:
1) Given that height of the stone is represented by a second-order polynomial, which depicts a parabola as graph. The best approach to determine the instant when stone reaches its highest is by vertex form, whose form is:
Where:
, 
- Instant and maximum height of the stone, measured in seconds and meters.
- Vertex constant, which must be negative as there is an absolute maximum, measured in meters per square second.
Let be , which is transformed into vertex form:
i) 
Given
ii) 
Distributive property/
iii) ![h = -5\cdot [(t^{2}-4\cdot t +4)+(-36)]](https://tex.z-dn.net/?f=h%20%3D%20-5%5Ccdot%20%5B%28t%5E%7B2%7D-4%5Ccdot%20t%20%2B4%29%2B%28-36%29%5D)
Existence of additive inverse/Definitions of addition and subtraction
iv) 
Distributive property/
/Perfect square binomial
v) Compatibility with addition/Existence of additive inverse/Modulative property/Definition of subtraction/Result
The vertex form of is .
2) The time can be extracted from previous results, which indicates that stone reaches its maximum height 2 seconds after being thrown.
