What is the vertex of #y= -3x^2 + 2x − 4#?

2 Answers
Bill Jorgensen
May 21, 2018

#vertex (1/3, -11/3)#

Explanation:

#a^2 + bx +c#

#y= -3x^2 + 2x − 4#

a = -3
b=2
c=-4

vertex is #(h, k)#

#h = (-b)/(2a)#

#k = f(h)# i.e. put what you found for h back into your function as x and solve for y.

#h = (-2)/(2*-3) = 1/3#

#k = (-3*1/3)^2 + 2*1/3 − 4 = -11/3#

#vertex (1/3, 1/3)#

Jim G.
May 21, 2018

#"vertex "=(1/3,-11/3)#

Explanation:

#"given the equation in standard form ";y=ax^2+bx+c#

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

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

#y=-3x^2+2x-4" is in standard form"#

#"with "a=-3,b=2" and "c=-4#

#rArrx_("vertex")=-2/(-6)=1/3#

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

#y=-3(1/3)^2+2/3-4#

#color(white)(y)=-1/3+2/3-12/3=-11/3#

#rArrcolor(magenta)"vertex "=(1/3,-11/3)#

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