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

Algebra ->  Quadratic Equations and Parabolas -> 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       Log On


   

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:
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) Describe how this graph compares to the graph of y = x2?
Answer:

Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
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=%28x-3%29%5E2-1
Show work in this space.
y=%28x%5E2-6x%2B%28-6%2F2%29%5E2%29-%28-6%2F2%29%5E2%2B8
y=%28x%5E2-6x%2B%28-3%29%5E2%29-%28-3%29%5E2%2B8
y=%28x-3%29%5E2-9%2B8
y=%28x-3%29%5E2-1
:

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%28300%2C200%2C-10%2C10%2C-10%2C10%2C%28x-3%29%5E2-1%29
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%28300%2C200%2C-10%2C10%2C-10%2C10%2C%28x-3%29%5E2-1%2Cx%5E2%29
Happy Calculating!!!