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

##### 2 Answers

To complete the square of

Take out the

Within the brackets, divide the second term by 2 and write it like this without getting rid of the second term:

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:

Then simplify:

You can conclude from this that the vertex is

#### Explanation:

#"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"#