# 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