Simplify: 3x + 6y - (4x - 2y)
1 answer:
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Answer:
Step-by-step explanation:
Completing the square is a method of rewriting a quadratic equation in the standard form such that it is in vertex form. The first step is to group the linear and quadratic terms, then factor out the coefficient of the quadratic term. After doing so, complete the square, add a value such that the linear and quadratic terms form a perfect square trinomial. Do not forget to balance the equation. The final step is to simplify.
Group,
Complete the square,
Simplify,
Now solve the equation using inverse operations,
Notice that our function 
is a parabola, and the vertex form of a parabola is:
where (h,k) are the coordinates of its vertex.
The first thing we need to do is find the vertex (h,k) and to do that we are going to use the vertex formula:
, and then we are going to evaluate our function at 
to find 
.
We know for our problem that
, and 
, so lets replace those values in our vertex formula to find :
Now, we are going to evaluate our function at -6 to find:
Now that we have our vertex, where and ; lets replace those values in our vertex form equation:
![f(x)=-5[x-(-6)]^{2} +(-1)](https://tex.z-dn.net/?f=f%28x%29%3D-5%5Bx-%28-6%29%5D%5E%7B2%7D%20%2B%28-1%29)
We can conclude that the vertex form of our function is, and its vertex is (-6,-1).
The first thing we need to do is find the vertex (h,k) and to do that we are going to use the vertex formula:
We know for our problem that
Now, we are going to evaluate our function at -6 to find
Now that we have our vertex, where
We can conclude that the vertex form of our function is