# How do you find the vertex of #f(x)=-5x^2+2x+7#?

##### 1 Answer

May 6, 2017

#### Explanation:

#"for the standard quadratic function"#

#• y=ax^2+bx+c; a!=0#

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

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

#"for " f(x)=-5x^2+2x+7#

#a=-5,b=2" and " c=7#

#rArrx_(color(red)"vertex")=-2/(-10)=1/5#

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

#rArry_(color(red)"vertex")=-5(1/5)^2+2(1/5)+7#

#color(white)(rArryverte)=-1/5+2/5+35/5=36/5#

#rArrcolor(magenta)"vertex " =(1/5,36/5)#