Respuesta :
Answer:
This means that the coordinates of the vertex of the function are [tex](6,-31)[/tex]
Step-by-step explanation:
To find the x-coordinate of the vertex of a quadratic function, we can use the formula:
[tex]x=\frac{-b}{2a}[/tex]
We are given the function [tex]f(x)=x^2-12x+5[/tex]
In this function, [tex]a=1[/tex] and [tex]b=-12[/tex]
Now we can input these values into our formula
[tex]x=\frac{-(-12)}{2(1)} \\\\x=\frac{12}{2} \\\\x=6[/tex]
This means that the x-value of the vertex is located at [tex]x=6[/tex]. To find the other half of the coordinate pair, we can now plug [tex]x=6[/tex] into the given function
[tex]f(6)=(6)^2-12(6)+5\\\\f(6)=36-72+5\\\\f(6)=41-72\\\\f(6)=-31[/tex]
This means that the coordinates of the vertex of the function are [tex](6,-31)[/tex]