Question 316527
Complete the square to get to vertex form.
{{{y=a(x-h)^2+k}}}
where (h,k) is the vertex.
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{{{x^2 + 4x + 7=(x^2+4x+4)+3}}}
{{{x^2 + 4x + 7=(x+2)^2+3}}}
The vertex is (-2,3)
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Now set the equation equal to zero to solve for the zeros.
{{{(x+2)^2+3=0}}}
{{{(x+2)^2=-3}}}
{{{x+2=0 +- sqrt(3)i}}}
{{{x=-2 +- sqrt(3)i}}} where {{{i=sqrt(-1)}}}