Question 453211


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



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



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



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



{{{x=1/2}}} Reduce.



So the x-coordinate of the vertex is {{{x=1/2}}}. Note: this means that the axis of symmetry is also {{{x=1/2}}}.



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



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



{{{y=3(1/2)^2-3(1/2)+2}}} Plug in {{{x=1/2}}}.



{{{y=3(1/4)-3(1/2)+2}}} Square {{{1/2}}} to get {{{1/4}}}.



{{{y=3/4-3(1/2)+2}}} Multiply {{{3}}} and {{{1/4}}} to get {{{3/4}}}.



{{{y=3/4-3/2+2}}} Multiply {{{-3}}} and {{{1/2}}} to get {{{-3/2}}}.



{{{y=5/4}}} Combine like terms.



So the y-coordinate of the vertex is {{{y=5/4}}}.



So the vertex is *[Tex \LARGE \left(\frac{1}{2},\frac{5}{4}\right)].