# How to describe the relationship between the graph of #f(x) x^2_2x+6# and the graph of #y=x^2#?

##### 1 Answer

Feb 28, 2017

the graph of

#### Explanation:

To examine the relationship we need to complete the square of the first function:

# f(x) = x^2-2x+6 #

# \ \ \ \ \ \ \ = (x-1)^2 -(1)^2+6 #

# \ \ \ \ \ \ \ = (x-1)^2 -1+6 #

# \ \ \ \ \ \ \ = (x-1)^2+5 #

And so the graph of

We can see this graphically:

**Graph of #y=x^2#**

graph{ x^2 [-10, 10, -2, 15] }

**Graph of #y=f(x)#**

graph{ x^2-2x+6 [-10, 10, -2, 15] }