What is the vertex form of #y=3x^2-2x-1 #?
3 Answers
Explanation:
Given a quadratic of the form
To find
So the vertex is
Vertex form 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 "color(blue)"completing the square"#
#• " the coefficient of the "x^2" term must be 1"#
#rArry=3(x^2-2/3x-1/3)#
#• " add/subtract "(1/2"coefficient of x-term")^2" to"#
#x^2-2/3x#
#y=3(x^2+2(-1/3)xcolor(red)(+1/9)color(red)(-1/9)-1/3)#
#color(white)(y)=3(x-1/3)^2+3(-1/9-3/9)#
#rArry=3(x-1/3)^2-4/3larrcolor(red)"in vertex form"#
Explanation:
You must complete the square to put this quadratic into turning point form.
First, factorise out the
Then halve the
Note that the polynomial inside the brackets is a perfect square. The extra
Hence:
From this the turning point can be found to be located at