Question 143722: 1. Solve  by completing the square. Find exact solutions.
Then:
a. Find the vertex.
b. Find the line of symmetry.
c. Determine whether there is a maximum or minimum value and find that value.
d. Show a sketch of the graph.
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Start with the given equation
Take half of the x-coefficient 8 to get 4 (ie  )
Now square 4 to get 16. (ie  )
 Add this result to both sides
 Combine like terms
 Factor  to get  . (note: if you need help with factoring, check out this solver)
 Take the square root of both sides
 Subtract 4 from both sides
 Simplify  to get  . (note: If you need help with simplifying square roots, check out this solver)
So the solutions are
 or 
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a)
Start with the given equation
 Subtract 11 from both sides
To find the vertex, we first need to find the axis of symmetry (ie the x-coordinate of the vertex)
To find the axis of symmetry, use this formula:
From the equation  we can see that a=1 and b=8
 Plug in b=8 and a=1
 Multiply 2 and 1 to get 2
 Reduce
So the axis of symmetry is
So the x-coordinate of the vertex is . Lets plug this into the equation to find the y-coordinate of the vertex.
Lets evaluate 
 Start with the given polynomial
 Plug in
 Raise -4 to the second power to get 16
 Multiply 8 by -4 to get -32
 Now combine like terms
So the vertex is (-4,-27)
b)
From part a) we found the axis of symmetry to be
c)
Looking at , we can see that  ,  , and  . Since  , this tells us that the parabola opens upward and that there is a minimum.
To find the minimum, we only need to look at the vertex. Since the vertex is the point (-4,-27), this means that the minimum is 
d)
Here's a sketch to visually verify our answers
 Graph of
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