Question 172428


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^2-20x+4}}}, we can see that {{{a=1}}}, {{{b=-20}}}, and {{{c=4}}}.



{{{x=(-(-20))/(2(1))}}} Plug in {{{a=1}}} and {{{b=-20}}}.



{{{x=(20)/(2(1))}}} Negate {{{-20}}} to get {{{20}}}.



{{{x=(20)/(2)}}} Multiply 2 and {{{1}}} to get {{{2}}}.



{{{x=10}}} Divide.



So the x-coordinate of the vertex is {{{x=10}}}. Note: this means that the axis of symmetry is also {{{x=10}}}.



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



{{{y=x^2-20x+4}}} Start with the given equation.



{{{y=(10)^2-20(10)+4}}} Plug in {{{x=10}}}.



{{{y=100-20(10)+4}}} Square {{{10}}} to get {{{100}}}.



{{{y=100-200+4}}} Multiply {{{-20}}} and {{{10}}} to get {{{-200}}}.



{{{y=-96}}} Combine like terms.



So the y-coordinate of the vertex is {{{y=-96}}}.



So the vertex is *[Tex \LARGE \left(10,-96\right)].