Question

What is the vertex of `y=x^2-12x+16`?

Answer 1

`"vertex "=(6,-20)`

Explanation:

`"given a quadratic in "color(blue)"standard form"`

`•color(white)(x)y=ax^2+bx+c color(white)(x);a!=0`

`"then the x-coordinate of the vertex is"`

`•color(white)(x)x_(color(red)"vertex")=-b/(2a)`

`y=x^2-12x+16" is in standard form"`

`"with "a=1,b=-12" and "c=16`

`x_("vertex")=-(-12)/2=6`

`"substitute "x=6" into the equation for y-coordinate"`

`y_("vertex")=36-72+16=-20`

`color(magenta)"vertex "=(6,-20)`