Question

How do you find the vertex of the parabola `y=x^2-2x-8`?

Answer 1

`(1,-9)`

Explanation:

`"for the standard form of a parabola " y=ax^2+bx+c`

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

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

`y=x^2-2x-8" is in standard form"`

`"with " a=1,b=-2" and " c=-8`

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

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

`rArry_(color(red)"vertex")=1-2-8=-9`

`rArrcolor(magenta)"vertex "=(1,-9)`
graph{x^2-2x-9 [-32.42, 32.53, -16.34, 16.15]}