Question 189898


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}}}, we can see that {{{a=3}}}, {{{b=0}}}, and {{{c=0}}}.



{{{x=(-(0))/(2(3))}}} Plug in {{{a=3}}} and {{{b=0}}}.



{{{x=(-0)/(6)}}} Multiply 2 and {{{3}}} to get {{{6}}}.



{{{x=0}}} Divide.



So the x-coordinate of the vertex is {{{x=0}}}. Note: this means that the axis of symmetry is also {{{x=0}}}.



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}}} Start with the given equation.



{{{y=3(0)^2}}} Plug in {{{x=0}}}.



{{{y=3(0)}}} Square {{{0}}} to get {{{0}}}.



{{{y=0}}} Multiply {{{3}}} and {{{0}}} to get {{{0}}}.




So the y-coordinate of the vertex is {{{y=0}}}.



So the vertex is *[Tex \LARGE \left(0,0\right)].