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The vertex form: y = a(x - h)2 + k where (h, k) is the vertex.
y = x2 + 4x + 7 add and subtract 4 to the right side to complete the square
y = x2 + 4x + 4 - 4 + 7 form the square
y = (x + 2)2 + 3 write + 2 = -(-2)
y = [x - (-2)]2 + 3
Thus, the vertex is (-2, 3)
4x-x2 = 2
6
A completely factored form is one which is composed of product of factors and can't be factorized further. Let us consider two examples: x2 - 4x + 4 is not a factored form because it can be factored as (x - 2)(x - 2). (x +1)(x2 - 4x + 4) is also not a factored form because x2 - 4x + 4 can be factored further as (x - 2)(x - 2). So, the completely factored form is (x + 1)(x - 2)(x - 2).
X2 + 4xx(x + 4)=======
The vertex form is y = (x - 4)2 + 13