Question 55873
Hi Tine,
For the function {{{y  =  x^2 - 6x + 8}}}, perform the following tasks:
a) 	Put the function in the form y = a(x - h)2 + k.
Answer:  
Show work in this space.  
y=(x^2-6x+____)-___+8
The blanks are fillied with {{{c=(b/2)^2}}}
{{{c=((-6)/2)^2}}}
{{{c=(-3)^2}}}
c=9
{{{y=(x^2-6x+9)-9+8}}}  Factor your perfect square trinomial.
{{{y=(x-3)^2-1}}}
b) 	What is the equation for the line of symmetry for the graph of this function?
Answer:  When the quadratic equation is in {{{y=a(x-h)^2+k}}}, the line of symmetry is x=h.  In this equation h=3, so the line of symmetry is 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.   
1. The vertex is (h,k)=(3,-1)
2. When a is positive the parabola opens up like a U, if it's negative, it opens down like an n.  a=+1, so ours opens up.
3. If a>1, then it's skinnier (stretched vertically).  If {{{-1<a<1}}}, then it's wider (shrunk vertically).  a=1 in this case so it has a standard width.

{{{graph(300,200,-10,10,-10,10,(x-3)^2-1)}}}


Explanation of graphing.  


d) 	In your own words, describe how this graph compares to the graph of y = x2?
Answer:  It is the same shape shifted horizontally h units (h=3, so 3 units to the right) and vertically k units (k=-1, so 1 unit down.)
See for yourself:
{{{graph(300,200,-10,10,-10,10,(x-3)^2-1,x^2)}}}
Happy Calculating!!!