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

2 Answers
Jan 13, 2018

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)

Jan 13, 2018

y=-3(x-2/3)^2-5/3

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"