Question 29638: I need help solving  by completing the perfect square to get exact solutions. Based on the solutions I then need to describe the position of the graph of F(x)= on the x-y plane.
Answer by longjonsilver(2297)   (Show Source):
You can put this solution on YOUR website! 
Now complete this square on the LHS:
2a = 3/2
--> a = 3/4
--> 
--> 
So,  or 
 or 
 or 
 or 
Well, you have a square root of a negative number, so this is nothing "real". In essence, there are no solutions... the quadratic does not cross the x-axis and will lie above it. As to where it lies, well the work done to get the equation in the form  tells us that the vertex lies at x=(-3/4).
Now, for the original equation,  , when we put this value of x in, we get y=7/8... the 7/16 in the "completed the square" version of the equation is a scaled version...because we divided everything by 2, if you remember.
If we plot the original curve, this is confirmed:
jon.
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