Question

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

Answer 1

`"vertex "=(1/2,63/4)`

Explanation:

`"given a quadratic in standard form"color(white)(x)ax^2+bx+c`

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

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

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

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

`rArrx_("vertex")=-(-1)/2=1/2`

`"substitute this value into the equation for y"`

`y_("vertex")=(1/2)^2-1/2+16=63/4`

`rArrcolor(magenta)"vertex "=(1/2,63/4)`