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

Question

Savannah Anderson · Accepted Answer

To complete the square of #-3x^2+4x-3#:
Take out the #-3#
#y=-3(x^2-4/3x)-3#
Within the brackets, divide the second term by 2 and write it like this without getting rid of the second term:
#y=-3(x^2-4/3x+(2/3)^2-(2/3)^2)-3#
These terms cancel each other out so adding them to the equation isn't a problem. Then within the brackets take the first term, the third term, and the sign preceding the second term, and arrange it like this:
#y=-3((x-2/3)^2-(2/3)^2)-3#
Then simplify:
#y=-3((x-2/3)^2-4/9)-3#
#y=-3(x-2/3)^2+4/3-3#
#y=-3(x-2/3)^2-5/3# You can conclude from this that the vertex is #(2/3, -5/3)#

Eva Adamson · Answer

#y=-3(x-2/3)^2-5/3# #"the equation of a parabola in "color(blue)"vertex form"# is. #color(red)(bar(ul(|color(white)(2/2)color(black)(y=a(x-h)^2+k)color(white)(2/2)|)))# #"where "(h,k)" are the coordinates of the vertex and a"# #"is a multiplier"# #"to obtain this form use the method of "color(blue)"completing the square"# #• " the coefficient of the "x^2" term must be 1"# #rArry=-3(x^2-4/3x+1)# #• " add/subtract "(1/2"coefficient of x-term")^2" to"# #x^2-4/3x# #y=-3(x^2+2(-2/3)xcolor(red)(+4/9)color(red)(-4/9)+1)# #color(white)(y)=-3(x-2/3)^2-3(-4/9+1)# #color(white)(y)=-3(x-2/3)^2-5/3larrcolor(red)"in vertex form"#

Ethan Adkins · Answer

undefined The vertex form of the quadratic function $y = -3x^2 + 4x - 3$ is $y = -3(x - \frac{2}{3})^2 - \frac{17}{3}$.