SOLUTION: 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

Click here to see ALL problems on Graphs

Question 142976: 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 3 to get . Now square to get . Add this number to both sides

Add 18 and to get

Factor the left side. Now the left side is a complete square

Take the square root of both sides

or Simplify and expand

or Add to both sides in each case

or Combine like terms

or Reduce

So the solutions are or

-----------------------------------------------------------------

a)

Start with the completed square

Subtract from both sides

Now the equation is in vertex form where the vertex is (h,k)

So in this case, the vertex is

b)

The line of symmetry is simply the equation where h is the x-coordinate of the vertex. So the axis of symmetry is

c)

Remember, we're still using the general form ,
Looking at , we can see that . Since , this means that the parabola opens up and there is a minimum. So the minimum occurs at the vertex which means that the minimum is

d)

Finally here's a sketch to visually verify our answers