SOLUTION: Totally lost. Thanks for any help. 2) 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

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: Totally lost. Thanks for any help. 2) 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       Log On


   

Question 35606: Totally lost. Thanks for any help.
2) 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 rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
You will need to complete the square to write this in the correct form.
y+=+x%5E2+-+6x+%2B+8

Take half of the x coefficient and square it. Next, add AND subtract it from the same side. In this way you will NOT change the equation:
y+=+x%5E2+-+6x+%2B+____+-+_____+%2B+8

Half of -6 is -3, and (-3) squared will be 9, so add and subtract 9 from the right side of the equation:
y+=+x%5E2+-+6x+%2B+____+-+_____+%2B+8
y+=+x%5E2+-+6x+%2B+9+-+9+%2B+8

This forms a perfect square trinomial in the first three terms on the right side:
y+=+%28x-3%29%5E2+-1

So a = 1, h= 3, and k= -1.

The line of symmetry is x= 3.

The graph is a parabola with vertex at (3,-1).
graph%28300%2C300%2C+-10%2C10%2C-10%2C10%2C+x%5E2-6x%2B8%29+

Compared to the graph of y = x^2, this graph is exactly the same shape. The vertex is just moved from (0,0) to (3,-1). Here is a comparision:
graph%28300%2C300%2C+-10%2C10%2C-10%2C10%2C+x%5E2-6x%2B8%2C+x%5E2%29+

R^2 at SCC