How do you find the coordinates of the vertex #y= -6x^2 + 14x#?

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Answer 1 · 2016-08-13T11:15:08

#P=(7/6,10.5)#

#y=-6x^2+14x#

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#"Let the coordinates of vertex be "P(x,y)#

#"Take derivative of the function "#

#(d y)/(d x)=-12x+14#

#"Now calculate "(d y)/(d x)=0#

#-12x+14=0#

#12x=14#

#x=14/12=7/6 " (This is the x coordinate of vertex)"#

#"calculate "f(x) " to find the y coordinate of vertex"#

#"plug x=" 7/6 " into y"#

#y=-6*(7/6)^2+14*7/6#

#y=-49/6+98/6#

#y=49/6#

#y=("This is the y coordinate of vertex")#

#"Thus"#

#P=(7/6,8.17)#