Question 188526

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+6x+8}}}, we can see that {{{a=1}}}, {{{b=6}}}, and {{{c=8}}}.



{{{x=(-(6))/(2(1))}}} Plug in {{{a=1}}} and {{{b=6}}}.



{{{x=(-6)/(2)}}} Multiply 2 and {{{1}}} to get {{{2}}}.



{{{x=-3}}} Divide.



So the x-coordinate of the vertex is {{{x=-3}}}. Note: this means that the axis of symmetry is also {{{x=-3}}}.



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



{{{y=x^2+6x+8}}} Start with the given equation.



{{{y=(-3)^2+6(-3)+8}}} Plug in {{{x=-3}}}.



{{{y=1(9)+6(-3)+8}}} Square {{{-3}}} to get {{{9}}}.



{{{y=9+6(-3)+8}}} Multiply {{{1}}} and {{{9}}} to get {{{9}}}.



{{{y=9-18+8}}} Multiply {{{6}}} and {{{-3}}} to get {{{-18}}}.



{{{y=-1}}} Combine like terms. Note: 9-18=-9 and -9+8=-1



So the y-coordinate of the vertex is {{{y=-1}}}.



So the vertex is *[Tex \LARGE \left(-3,-1\right)].



So you were off by a sign.