Question 158118


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=2x^2-12x+6}}}, we can see that {{{a=2}}}, {{{b=-12}}}, and {{{c=6}}}.



{{{x=(-(-12))/(2(2))}}} Plug in {{{a=2}}} and {{{b=-12}}}.



{{{x=(12)/(2(2))}}} Negate {{{-12}}} to get {{{12}}}.



{{{x=(12)/(4)}}} Multiply 2 and {{{2}}} to get {{{4}}}.



{{{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=2x^2-12x+6}}} Start with the given equation.



{{{y=2(3)^2-12(3)+6}}} Plug in {{{x=3}}}.



{{{y=2(9)-12(3)+6}}} Square {{{3}}} to get {{{9}}}.



{{{y=18-12(3)+6}}} Multiply {{{2}}} and {{{9}}} to get {{{18}}}.



{{{y=18-36+6}}} Multiply {{{-12}}} and {{{3}}} to get {{{-36}}}.



{{{y=-12}}} Combine like terms.



So the y-coordinate of the vertex is {{{y=-12}}}.



So the vertex is *[Tex \LARGE \left(3,-12\right)].