SOLUTION: 2) For the function y = x2 - 4x - 5, 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 t

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Question 53229: 2) For the function y = x2 - 4x - 5, 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

Answer by funmath(2933)   (Show Source): You can put this solution on YOUR website!
a) You need to make a perfect square trinomial in such a way that you don't change the value of the function. Make sure that if you add anything you also take it away. Right now this is the standard form of a parabola right now.
a)

To find the number that makes a perfect square take




=4 Add 4 to the inside of the parenthesis and take 4 away from the outside of the parenthesis.


Now the parenthesis has a perfect square:

Now this is the vertex form of a parabola!
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b) puts the parabolic function in a form that makes the vertex and the axis of symmetry easy to see.
The vertex is (h,k)
the axis of symmetry is x=h
In our case h=2, so our axis of symmetry is x=2.
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c) Plot the vertex and y intercept (if it's in a reasonable place), if your asked for more points add and take away 1 from the axis of symmetry and plu that into your function to find the y-values.
Vertex=(2,-9)
------------------
y-int: y=(0-2)^2-9
y=4-9=-5
(0,-5)

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d) It's shifted right two units and down 9 units. Observe:


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