SOLUTION: 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 line

Algebra ->  Rational-functions -> SOLUTION: 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 line      Log On


   

Question 28424: 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 line of symmetry?
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 the graph of y = x2?
Answer:



Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
y++=++x%5E2+-+6x+%2B+8 needs to be converted to a version that has duplicate factors. It is called "completing the square". To do this, we will look at just y++=++x%5E2+-+6x and see what third number we need to add to it.

If i added +9 to the above equation, giving y++=++x%5E2+-+6x+%2B+9, then this can be factorised as y=%28x-3%29%5E2. This is the form i want. So...

y++=++x%5E2+-+6x+%2B+8 becomes y++=++x%5E2+-+6x++%2B+9+-+9+%2B+8. Can you see that i have added in a "+9" and a "-9", so overall, the equation is unchanged...i am just messing it around a bit.

y++=++x%5E2+-+6x++%2B+9+-+9+%2B+8 becomes
y++=++%28x-3%29%5E2+-+9+%2B+8 and finally
y++=++%28x-3%29%5E2+-+1 which is
y++=++%28x-3%29%5E2+%2B+%28-1%29

This is the form the Q wanted. As to why? well, in this form, the 3 and the -1 tell us the position of the turning point in the quadratic..the point where the curve turns... it is at (3,-1)

so the line of symmetry is x=3

No need to plot the graph, we can sketch it... we know the turning point. Only other things to know are where does the curve cross the x- and y-axes?

Crossing the y-axis is when x=0
y++=++x%5E2+-+6x+%2B+8 becomes
y++=++%280%29%5E2+-+6%280%29+%2B+8
--> y = 8

Crossing the x-axis is when y=0
y++=++%28x-3%29%5E2+-+1 becomes
0++=++%28x-3%29%5E2+-+1
or %28x-3%29%5E2+-+1+=+0
%28x-3%29%5E2+=+1
%28x-3%29+=+sqrt%281%29+ OR %28x-3%29+=+-sqrt%281%29+
x-3 = 1 OR x-3 = -1
--> x = 4 OR x = 2

Graph is graph%28300%2C300%2C-3%2C6%2C-5%2C10%2Cx%5E2+-+6x+%2B+8%29

Compares to y=x%5E2 in the fact that it is the same curve just moved... how many units to the right? How many units down? You say.

jon.