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

Jul 23, 2017

$f {\left(x\right)}_{\min} = - 1$

line of symmetry$\text{ } X = 1$

#### Explanation:

You need to complete the square first before answering this question

$f \left(x\right) = {x}^{2} - 2 x - 1$

$f \left(x\right) = \left({x}^{2} - 2 x + {\left(- 1\right)}^{2}\right) - {\left(- 1\right)}^{2} - 1$

$f \left(x\right) = {\left(x - 1\right)}^{2} - 1 - 1$

$\therefore f \left(x\right) = {\left(x - 1\right)}^{2} - 2$

since we have a $+ {x}^{2} \text{ }$term the function will have a minimum.

this will be when ${\left(x - 1\right)}^{2} \text{ }$term$= 0$

$\therefore \text{ minimum } i s - 2$

the coordinates for the minimum$\left(1 , - 2\right)$

the axis of symmetry is the line through the vertex $i e . X = 1$

the results can be seen on the graph below

graph{x^2-2x-1 [-10, 10, -5, 5]}