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"#
