How do you find the axis of symmetry, graph and find the maximum or minimum value of the function f(x)=2x24x+1?

2 Answers
Feb 24, 2016

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 y=ax2+bx+c
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.

y=2x24x+1=2(x1)22+1=2(x1)21

This expression is at its minimum when x=1 (the bracketed term is zero) and so the vertex is (1,1)

The axis of symmetry is x=1
SketchSketch

Feb 24, 2016

A slightly 'cheating' sort of way to find that the axis of symmetry is at x=1

Explanation:

Given: 2x24x+1

Write as 2(x242x)+1

Now consider the 42x

Apply: (12)×(42)=+44=1

This is in fact, part of the process for completing the squarebut it is in disguise.

Now compare this to the graph
Tony BTony B