Question 164992


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+x-5}}}, we can see that {{{a=-3}}}, {{{b=1}}}, and {{{c=-5}}}.



{{{x=(-(1))/(2(-3))}}} Plug in {{{a=-3}}} and {{{b=1}}}.



{{{x=(-1)/(-6)}}} Multiply 2 and {{{-3}}} to get {{{-6}}}.



{{{x=1/6}}} Reduce.



So the x-coordinate of the vertex is {{{x=1/6}}}. Note: this means that the axis of symmetry is also {{{x=1/6}}}.



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+x-5}}} Start with the given equation.



{{{y=-3(1/6)^2+1/6-5}}} Plug in {{{x=1/6}}}.



{{{y=-3(1/36)+1/6-5}}} Square {{{1/6}}} to get {{{1/36}}}.



{{{y=-1/12+1/6-5}}} Multiply {{{-3}}} and {{{1/36}}} to get {{{-1/12}}}.



{{{y=-59/12}}} Combine like terms.



So the y-coordinate of the vertex is {{{y=-59/12}}}.



So the vertex is *[Tex \LARGE \left(\frac{1}{6},-\frac{59}{12}\right)].