Question 206764


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-13}}}, we can see that {{{a=-2}}}, {{{b=12}}}, and {{{c=-13}}}.



{{{x=(-(12))/(2(-2))}}} Plug in {{{a=-2}}} and {{{b=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-13}}} Start with the given equation.



{{{y=-2(3)^2+12(3)-13}}} Plug in {{{x=3}}}.



{{{y=-2(9)+12(3)-13}}} Square {{{3}}} to get {{{9}}}.



{{{y=-18+12(3)-13}}} Multiply {{{-2}}} and {{{9}}} to get {{{-18}}}.



{{{y=-18+36-13}}} Multiply {{{12}}} and {{{3}}} to get {{{36}}}.



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



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



So the vertex is *[Tex \LARGE \left(3,5\right)].