# How do you find the axis of symmetry, graph and find the maximum or minimum value of the function #f(x) = 2x^2 - 4x +1#?

##### 2 Answers

To find the vertex and the axis of symmetry, rearrange the equation into vertex form by completing the square.

#### Explanation:

This equation is for a parabola, because it follows the general form

Hence the maximum or minimum value is at the vertex. In this case, because the squared term is positive, it will be a minimum value.

To find the vertex and the axis of symmetry, rearrange the equation into vertex form by completing the square.

This expression is at its minimum when

The axis of symmetry is

A slightly 'cheating' sort of way to find that the axis of symmetry is at

#### Explanation:

Given:

Write as

Now consider the

Apply:

Now compare this to the graph