Question 378633


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=3x^2-12x+4}}}, we can see that {{{a=3}}}, {{{b=-12}}}, and {{{c=4}}}.



{{{x=(-(-12))/(2(3))}}} Plug in {{{a=3}}} and {{{b=-12}}}.



{{{x=(12)/(2(3))}}} Negate {{{-12}}} to get {{{12}}}.



{{{x=(12)/(6)}}} Multiply 2 and {{{3}}} to get {{{6}}}.



{{{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.



{{{y=3x^2-12x+4}}} Start with the given equation.



{{{y=3(2)^2-12(2)+4}}} Plug in {{{x=2}}}.



{{{y=3(4)-12(2)+4}}} Square {{{2}}} to get {{{4}}}.



{{{y=12-12(2)+4}}} Multiply {{{3}}} and {{{4}}} to get {{{12}}}.



{{{y=12-24+4}}} Multiply {{{-12}}} and {{{2}}} to get {{{-24}}}.



{{{y=-8}}} Combine like terms.



So the y-coordinate of the vertex is {{{y=-8}}}.



So the vertex is *[Tex \LARGE \left(2,-8\right)].



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