Question 172339
They arrived to that ANSWER by Completing the Square:
Here it goes:
Given --------->{{{y=x^2+4x+1}}}
{{{y=(x^2+4x+4)highlight(-4)+1}}}, Remember to add "+4" to make it a perfect square, and DON'T FORGET to subtract "-4" so it won't change the expression.
Why 4? Take "half" of the middle term constant (which is 4 = 4/2=2), then squared it ---> {{{2^2=highlight(4)}}}
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Continuing, {{{highlight(y=(x+2)^2-3)}}} Answer----> vertex form={{{a(x-h)^2+k}}}; {{{h=-2}}},{{{k=-3}}}>>> Vertex (-2,-3), As you see on the graph:
{{{drawing(400,400,-6,6,-6,6,grid(1),graph(400,400,-6,6,-6,6,x^2+4x+1),circle(-2,-3,.12))}}}
Thank you,
Jojo