SOLUTION: I need help in understanding "completing the square for a quadratic function" My problem is the following
Rewrite each function in the from f(x)=a(x-h)2 + k
(a) f(x)=x2 + 6x
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Question 284420: I need help in understanding "completing the square for a quadratic function" My problem is the following
Rewrite each function in the from f(x)=a(x-h)2 + k
(a) f(x)=x2 + 6x (b) f(x)=2x2 - 20x + 3
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
The first thing to think about is: What happens when I multiply )
by itself? I get 
. That is the definition of a perfect square trinomial.
What you are trying to accomplish, without changing the value of the function, is to create a perfect square trinomial. The process is to first factor the lead coefficient out of the first and second degree terms, divide the resulting first degree term coefficient by 2, square that value, add that value to the function, and add the opposite of that value to the function so that you don't change the value.
\ =\ x^2\ +\ 6x)
Lead coefficient is 1, so no factoring required
First degree coefficient is 6. 6 divided by 2 is 3. 3 squared is 9.
Add 9 and -9
\ =\ x^2\ +\ 6x\ +\ 9\ -\ 9)
Factor the perfect square trinomial:
\ =\ \left(x\ +\ 3\right)^2\ -\ 9)
Now I can tell by inspection that my parabola has a vertex at (-3, -9)
\ +\ 3)
\ +\ 3\ -\ 50)
^2\ -\ 47)
John
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