Question 66260
For the function y  =  x2 - 6x + 8, perform the following tasks:
a) 	Put the function in the form y = a(x - h)2 + k.
Answer: {{{y=(x-3)^2-1}}} 
Show work in this space.
{{{y=(x^2-6x+(-6/2)^2)-(-6/2)^2+8}}}
{{{y=(x^2-6x+(-3)^2)-(-3)^2+8}}}
{{{y=(x-3)^2-9+8}}}
{{{y=(x-3)^2-1}}}  
:


b) 	What is the equation for the line of symmetry for the graph of this function?
Answer:  
The formula is x=h
In this case x=3
:


c) 	Graph the function using the equation in part a.  Explain why it is not necessary to plot points to graph when using y = a (x - h) 2 + k.
Show graph here.   
{{{graph(300,200,-10,10,-10,10,(x-3)^2-1)}}}

Explanation of graphing.  
The vertex is (h,k)=(3,-1)
a=1, so the parabola is of standard width.
Because it's positive it opens upward.


d)  Describe how this graph compares to the graph of y = x2?
Answer:  
It has the same shape, but is shifted horizontally right 3 units because of the -3 and vertically down 1 unit because of the -1.
Here's the two on the same graph:
{{{graph(300,200,-10,10,-10,10,(x-3)^2-1,x^2)}}}
Happy Calculating!!!