# How do you find the vertex for # f(x)=1/3x^2#?

##### 2 Answers

#### Explanation:

To find the x-coordinate of the vertex use the formula

vertex = (0,0)

#### Explanation:

The basic 'building block' for quadratic functions is y

#= x^2# The graph of this function has it's vertex at (0,0) and is symmetrical about the y-axis, as shown. graph{x^2 [-10, 10, -5, 5]}

for the general situation : y

#= ax^2# The graph shown above has a = 1.

If a > 1 the graph retains it's vertex at (0,0) and its shape but 'closes inwards in a similar way to a flower bud closing.

If a < 0 , the vertex is still (0,0) and shape is similar but this time it 'opens outward like the bud opening.

I've put

graph{(y-1/3 x^2)(y-x^2)=0 [-10, 10, -5, 5]}