# What is the vertex form of #y= (x -1)(x/2 + 2) #?

##### 1 Answer

May 6, 2018

#### Explanation:

#"expand the factors using FOIL"#

#y=1/2x^2+3/2x-2#

#"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"#

#"factor out "1/2#

#y=1/2(x^2+3x-4)#

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

#x^2+3x#

#y=1/2(x^2+2(3/2)x color(red)(+9/4)color(red)(-9/4)-4)#

#color(white)(y)=1/2(x+3/2)^2+1/2(-9/4-4)#

#color(white)(y)=1/2(x+3/2)^2-25/8larrcolor(red)"in vertex form"#