SOLUTION: Can someone help me with this problem? I'm stuck!!! I'm in a class that is over my head. Help!!!!!!!!!!!!!!!!!!!! For the function y = x2

SOLUTION: Can someone help me with this problem? I'm stuck!!! I'm in a class that is over my head. Help!!!!!!!!!!!!!!!!!!!! For the function y = x2 - 6x + 8, perform the following tas

Question 79162: Can someone help me with this problem? I'm stuck!!! I'm in a class that is over my head. Help!!!!!!!!!!!!!!!!!!!!
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:

Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
a) Put the function into the form
To do this you will start with the given function and you will "complete the square".
Now subtract the constant (8) from both sides.
Now complete the square in the x-terms by adding the square of half the x-coefficient (that's ) to both sides.
Factor the right side.
Now subtract 1 from both sides.
Compare this with:

a = 1
h = 3
k = -1
b) The equation of the line of symmetry is given by:
, so in this case, since h = 3, the equation of the line of symmetry is:
This is a vertical line passing through the point (3, 0)
c) It is not necessary to plot points to graph the function in this form because:
1) You know the equation of the line of symmetry.
2) You know that the parabola opens upward because a>0 (a is positive).
3) You know (or can find) the location of the vertex of the parabola. Thi is given by (h, k) or (3, -1)
4) You can find the x- and y-intercepts of the function by:
x-intercepts: Set y = 0 and solve for x.
Add 1 to both sides.
Take the square root of both sides.

+ or - Add 3 to both sides.
and
and These are the x-intercepts.
y-intercept: Set x = 0 and solve for y.

This the y-intecept.
Here is the graph (in red): I'll add the graph of the function (in green) so you can compare the two.

d) I'll leave the explanation to you. Look at the two graphs and try to see what effects the values of h and k have on the placement of the second (green) graph compared to the first (red) graph.

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