Question

Question #89c39

Answer 1

`(2,9)`

Explanation:

`"given a quadratic in standard form"`

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

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

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

`f(x)=-x^2+4x+5" is in standard form"`

`"with "a=-1,b=4" and "c=5`

`rArrx_(color(red)"vertex")=-4/(-2)=2`

`"substitute this value into f(x) for y-coordinate"`

`rArry_(color(red)"vertex")=-(2)^2+4(2)+5=9`

`rArrcolor(magenta)"vertex "=(2,9)`
graph{-x^2+4x+5 [-20, 20, -10, 10]}

Answer 2

The vertex is `(2,9)`

Explanation:

given quadratic equation`:`
`f(x)=-x^2+4x+5`
from this `a=-1,b=4,c=5`
from the vertex formula`:`
`x=(-b)/(2a)rArrx=(-4)/(-2)rArrx=2`
let `y=-x^2+4x+5=f(x)->(1)`
put `x=2` in `(1)`
`rArry=-(2^2)+4(2)+5rArry=-4+8+5rArry=9`
hence the vertex is `(2,9)`