Question

What is the the vertex of `y = -x^2 + 2x +4`?

Answer 1

`(1,5)`

Explanation:

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

`"the x-coordinate of the vertex is " x_(color(red)"vertex")=-b/(2a)`

`y=-x^2+2x+4" is in standard form "`

`"with " a=-1,b=2,c=4`

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

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

`rArry_(color(red)"vertex")=-1+2+4=5`

`rArrcolor(magenta)"vertex "=(1,5)`
graph{-x^2+2x+4 [-10, 10, -5, 5]}