# What is the vertex form of #y=(3x-5)(6x-2) #?

##### 2 Answers

The vertex form of

#### Explanation:

First we must know what is meant by the vertex form of a quadratic function, which is

We, therefore, want

We have

Therefore

Therefore

The quadratic part, therefore, is

This gives

Therefore,

#### 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"#

#"expand the factors"#

#rArry=18x^2-36x+10#

#• " the coefficient of the "x^2" term must be 1"#

#"factor out 18"#

#y=18(x^2-2x+5/9)#

#• " add/subtract "(1/2"coefficient of the x-term")^2" to"#

#x^2-2x#

#y=18(x^2+2(-1)x color(red)(+1)color(red)(-1)+5/9)#

#color(white)(y)=18(x-1)^2+18(-1+5/9)#

#color(white)(y)=18(x-1)^2-8larrcolor(red)"in vertex form"#