Question

What is the vertex of `y= x^2 - 8x + 18`?

Answer 1

`"vertex "=(4,2)`

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^2-8x+18" is in standard form"`

`"with "a=1,b=-8" and "c=18`

`rArrx_("vertex")=-(-8)/2=4`

`"substitute into the equation for y-coordinate"`

`y_("vertex")=4^2-(8xx4)+18=2`

`rArrcolor(magenta)"vertex "=(4,2)`
graph{x^2-8x+18 [-10, 10, -5, 5]}