# What is the vertex form of #y= (x+2) (2x+5) #?

##### 1 Answer

Mar 10, 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"#

#y=(x+2)(2x+5)larrcolor(blue)"expand the factors"#

#color(white)(y)=2x^2+9x+10#

#"to obtain vertex form use "color(blue)"completing the square"#

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

#rArry=2(x^2+9/2x+5)#

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

#x^2+9/2x#

#rArry=2(x^2+2(9/4)xcolor(red)(+81/16)color(red)(-81/16)+5)#

#color(white)(y)=2(x+9/4)^2+2(-81/16+5)#

#color(white)(y)=2(x+9/4)^2-1/8larrcolor(red)"in vertex form"#