Distributive property of 2(x+5)
2 answers:
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Answer:
The equation of the parabola is , whose real vertex is
, not
.
Step-by-step explanation:
A parabola is a second order polynomial. By Fundamental Theorem of Algebra we know that a second order polynomial can be formed when three distinct points are known. From statement we have the following information:
,
,
From definition of second order polynomial and the three points described above, we have the following system of linear equations:
(1)
(2)
(3)
The solution of this system is: ,
,
. Hence, the equation of the parabola is
. Lastly, we must check if
belongs to the function. If we know that
, then the value of
is:
does not belong to the function, the real point is
.
The best way to approach this problem is to look at the graph of the given function. Replace values of x from 1 to 24 to indicate the numbers of hours in a day. As seen on the graph, there is only one point where the port is at high tide. That would be at 1:00 am.
Looking at the graph, it would be safe for the boats to be in the port when the graph levels off at around 10 to 24. That's from 10 am to before 12 midnight. Then, they would have to stay away between 12 midnight to before 10 am.
Looking at the graph, it would be safe for the boats to be in the port when the graph levels off at around 10 to 24. That's from 10 am to before 12 midnight. Then, they would have to stay away between 12 midnight to before 10 am.