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"