Question 644011
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+4}}}, we can see that {{{a=1}}}, {{{b=-6}}}, and {{{c=4}}}.



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



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



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



{{{f(3)=(3)^2-6(3)+4}}} Plug in {{{x=3}}}.



{{{f(3)=9-6(3)+4}}} Square {{{3}}} to get {{{9}}}.



{{{f(3)=9-18+4}}} Multiply {{{-6}}} and {{{3}}} to get {{{-18}}}.



{{{f(3)=-5}}} Combine like terms.



So the y-coordinate of the vertex is {{{y=-5}}}.



So the vertex is *[Tex \LARGE \left(3,-5\right)].