# What is the vertex form of #6y=(x + 13)(x - 3) #?

##### 1 Answer

Jan 8, 2018

#### 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"#

#6y=(x+13)(x-3)=x^2+10x-39#

#rArry=1/6(x^2+10x-39)#

#"using the method of "color(blue)"completing the square"#

#"on "x^2+10x-39#

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

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

#x^2+10x#

#x^2+2(5)xcolor(red)(+25)color(red)(-25)-39=(x+5)^2-64#

#rArry=1/6(x+5)^2-32/3#