What is the vertex of #y= -2x^2 + 2x + 9 #?

1 Answer
Jim G.
Jun 13, 2018

#"vertex "=(1/2,19/2)#

Explanation:

#"given a quadratic in standard form"#

#y=ax^2+bx+c;a!=0#

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

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

#y=-2x^2+2x+9" is in standard form"#

#"with "a=-2,b=2" and "c=9#

#x_("vertex")=-2/(-4)=1/2#

#"substitute this value into the equation for y"#

#y_("vertex")=-2(1/2)^2+2(1/2)+9=19/2#

#color(magenta)"vertex "=(1/2,19/2)#

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