Question 171912

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=x^2-13}}}, we can see that {{{a=1}}}, {{{b=0}}}, and {{{c=-13}}}.



{{{x=(-(0))/(2(1))}}} Plug in {{{a=1}}} and {{{b=0}}}.



{{{x=(-0)/(2)}}} Multiply 2 and {{{1}}} to get {{{2}}}.



{{{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=x^2-13}}} Start with the given equation.



{{{y=(0)^2-13}}} Plug in {{{x=0}}}.



{{{y=0-13}}} Square {{{0}}} to get {{{0}}}.



{{{y=-13}}} Combine like terms.



So the y-coordinate of the vertex is {{{y=-13}}}.



So the vertex is *[Tex \LARGE \left(0,-13\right)].