Question 55873: 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:
Show work in this space.
b) What is the equation for the line of symmetry for the graph of this function?
Answer:
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.
Explanation of graphing.
d) In your own words, describe how this graph compares to the graph of y = x2?
Answer:
Thank you tine
Found 2 solutions by funmath, venugopalramana:
Answer by funmath(2933)   (Show Source):
You can put this solution on YOUR website! Hi Tine,
For the function  , 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=9
 Factor your perfect square trinomial.
b) What is the equation for the line of symmetry for the graph of this function?
Answer: When the quadratic equation is in  , 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  .
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  , then it's wider (shrunk vertically). a=1 in this case so it has a standard width.
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:
Happy Calculating!!!
Answer by venugopalramana(3286)  (Show Source):
You can put this solution on YOUR website! see the following example and try
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Function y = x2 - 4x - 5, perform the
following tasks:
a) Put the function in the form y = a(x - h)2 + k.
b) What is the line of symmetry?
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.
Explanation of graphing.
d) In your own words, describe how this graph compares
to the graph of y = x2?
1 solutions
Answer 13849 by venugopalramana(1619) About Me on
2006-01-28 11:20:53 (Show Source):
Y=X^2-4X-5={(X-2)^2-4-5}=(X-2)^2-9
COMPARING WITH THE GIVEN EQN .
y=a(x-h)^2+k,WE INFER THAT
A=1,H=2 AND K=-9....THE LINE OF SYMMETRY IS X-2=0 AS
YOU WILL GET SAME VALUE OF Y WHETHER X-2=+4 SAY OR
-4...NAMELY,Y=7.
hence using the property of symmetry , vertex coordinates ,we can plot the graph without plotting all points
COMPARISON WITH Y=X^2 IS SHOWN BELOW
YOU CAN SEE THAT LINE OF SYMMETRY IS X=0 HERE.
ALSO THE MINIMUM VALUE OR VERTEX AT 0,0 IN CASE OF
Y=X^2,WHERE AS IT WAS AT (2,-9)
FOR THE GIVEN EQUATION---------------------------------------
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