How do you write the quadratic in vertex form given #y=-4x^2+12x+5#?

1 Answer
May 25, 2018

#y=-4(x-3/2)^2+14#

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

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

#"factor out "-4#

#y=-4(x^2-3x-5/4)#

#• " add/subtract "(1/2"coefficient of the x-term")^2" to"#
#x^2-3x#

#y=-4(x^2+2(-3/2)x color(red)(+9/4)color(red)(-9/4)-5/4)#

#color(white)(y)=-4(x-3/2)^2-4(-9/4-5/4)#

#color(white)(y)=-4(x-3/2)^2+14larrcolor(red)"in vertex form"#