Question #89c39

2 Answers
Jim G.
Jan 17, 2018

#(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]}

Manasvini Nittala
Jan 17, 2018

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)#

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