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You have to complete the square to get it into vertex form. Do this by setting the function equal to zero and at the same time moving the constant over to the other side of the equals sign so you have this: 
. Now we can complete the square on the polynomial by taking half the linear term, squaring it, and adding it to both sides. Our linear term is 4. Half of 4 is 2, and 2 squared is 4, so we add 4 to both sides: 
and simplify to get 
. In this process we have created a perfect square binomial on the left, which happens to be 
. Now move the -6 back over by addition to get 
. The vertex is found at (-2, 6), the third choice down.
Answer:
Part A: The graph of given inequality is shown below.
Part B: The point (4,6) is not a solution of given system of inequalities.
Step-by-step explanation:
Part A:
The given inequalities are
The related equation of given inequalities are
Put x=0, to find the y-intercepts.
Put y=0, to find the x-intercepts.
The x and y-intercepts of first line are (0,3) and (-1.5,0) respectively. The x and y-intercepts of second line are (0,-4) and (-2.667,0) respectively.
Check the given inequality by (0,0).
This statement is false. It means (0,0) is not the solution of this inequality and the shaded region is opposite side of the origin.
This statement is false. It means (0,0) is not the solution of this inequality and the shaded region is opposite side of the origin.
The graph of given inequalities is shown below.
Part B:
We have to check whether (4,6) is a solution of the system of inequality or not.
Check the given inequality for the point (4,6).
This statement is false. It means (4,6) is not the solution of given system of inequalities.
