How do you find the coordinates of the vertex #y= -3x^2 + 8x#?

1 Answer
Feb 22, 2017

#(4/3,16/3)#

Explanation:

The #color(blue)"standard quadratic function"# is.

#color(red)(bar(ul(|color(white)(2/2)color(black)(y=ax^2+bx+c; a≠0)color(white)(2/2)|)))#

#"for "y=-3x^2+8x#

#a=-3,b=8" and "c=0#

The x-coordinate of the vertex can be found using.

#color(red)(bar(ul(|color(white)(2/2)color(black)(x_("vertex")=-b/(2a))color(white)(2/2)|)))#

#rArrx_("vertex")=-8/(-6)=4/3#

Substitute this value into the equation to obtain the corresponding y-coordinate.

#y_("vertex")=-3(4/3)^2+8(4/3)#

#color(white)(y_("vertex"))=(-3xx16/9)+32/3#

#color(white)(y_("vertex"))=-16/3+32/3#

#color(white)(y_("vertex"))=16/3#

#rArr"coordinates of vertex "=(4/3,16/3)#
graph{-3x^2+8x [-20, 20, -10, 10]}