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

Algebra ->  Quadratic Equations and Parabolas -> 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      Log On


   

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) About Me  (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)y=x%5E2-4x-5
y=%28x%5E2-4x%29-5
To find the number that makes a perfect square take
%28%281%2F2%29b%29%5E2
%28%281%2F2%29%28-4%29%29%5E2
%28-4%2F2%29%5E2
%28-2%29%5E2
=4 Add 4 to the inside of the parenthesis and take 4 away from the outside of the parenthesis.
y=%28x%5E2-4x%2B4%29-5-4
y=%28x%5E2-4x%2B4%29-9
Now the parenthesis has a perfect square:
y=%28x-2%29%5E2-9
Now this is the vertex form of a parabola!
-----------------------------------------------------------
b)y=a%28x-h%29%5E2%2Bk 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.
----------------------------------------------------------------
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)
graph%28300%2C200%2C-10%2C10%2C-12%2C10%2Cy=%28x-2%29%5E2-9%29
---------------------------------------------------
d) It's shifted right two units and down 9 units. Observe:
graph%28300%2C200%2C-10%2C10%2C-12%2C10%2Cy=%28x-2%29%5E2-9%2Cx%5E2%29