Question 193063


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+8x+27}}}, we can see that {{{a=1}}}, {{{b=8}}}, and {{{c=27}}}.



{{{x=(-(8))/(2(1))}}} Plug in {{{a=1}}} and {{{b=8}}}.



{{{x=(-8)/(2)}}} Multiply 2 and {{{1}}} to get {{{2}}}.



{{{x=-4}}} Divide.



So the x-coordinate of the vertex is {{{x=-4}}}. Note: this means that the axis of symmetry is also {{{x=-4}}}.



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+8x+27}}} Start with the given equation.



{{{y=(-4)^2+8(-4)+27}}} Plug in {{{x=-4}}}.



{{{y=1(16)+8(-4)+27}}} Square {{{-4}}} to get {{{16}}}.



{{{y=16+8(-4)+27}}} Multiply {{{1}}} and {{{16}}} to get {{{16}}}.



{{{y=16-32+27}}} Multiply {{{8}}} and {{{-4}}} to get {{{-32}}}.



{{{y=11}}} Combine like terms.



So the y-coordinate of the vertex is {{{y=11}}}.



So the vertex is *[Tex \LARGE \left(-4,11\right)].