SOLUTION: Find the vertex and the equation of the line of symmetry for {{{f(x)=(1/3)x^2}}}

Question 130761: Find the vertex and the equation of the line of symmetry for
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation

Add to the equation. Note: this does not change the equation

From the equation we can see that and

Plug in and

Simplify

Divide

So the x-coordinate of the vertex is . This means that the equation of the line of symmetry is

Lets plug this into the equation to find the y-coordinate of the vertex.

Lets evaluate

Start with the given equation

Plug in

Raise 0 to the second power to get 0

Multiply and 0 to get 0

So the y-coordinate of the vertex is

So the vertex is (0,0)

If we graph the equation, we can visually verify our answer.

Graph of with a vertex of (0,0) and the line of symmetry of (blue line)
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