Question 577888
In order to find the vertex, we first need to find the x-coordinate of the vertex.



To find the x-coordinate of the vertex, use this formula: {{{x=(-b)/(2a)}}}.



{{{x=(-b)/(2a)}}} Start with the given formula.



From {{{y=x^2+4x+6}}}, we can see that {{{a=1}}}, {{{b=4}}}, and {{{c=6}}}.



{{{x=(-(4))/(2(1))}}} Plug in {{{a=1}}} and {{{b=4}}}.



{{{x=(-4)/(2)}}} Multiply 2 and {{{1}}} to get {{{2}}}.



{{{x=-2}}} Divide.



So the x-coordinate of the vertex is {{{x=-2}}}. Note: this means that the axis of symmetry is also {{{x=-2}}}.



Now that we know the x-coordinate of the vertex, we can use it to find the y-coordinate of the vertex.



{{{f(x)=x^2+4x+6}}} Start with the given equation.



{{{f(-2)=(-2)^2+4(-2)+6}}} Plug in {{{x=-2}}}.



{{{f(-2)=1(4)+4(-2)+6}}} Square {{{-2}}} to get {{{4}}}.



{{{f(-2)=4+4(-2)+6}}} Multiply {{{1}}} and {{{4}}} to get {{{4}}}.



{{{f(-2)=4-8+6}}} Multiply {{{4}}} and {{{-2}}} to get {{{-8}}}.



{{{f(-2)=2}}} Combine like terms.



So the y-coordinate of the vertex is {{{y=2}}}.



So the vertex is *[Tex \LARGE \left(-2,2\right)].