# What is the the vertex of #y = -12x^2+6x-18 #?

##### 1 Answer

Sep 30, 2017

#### 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 express "y=-12x^2+6x-18" in this form"#

#"we can use the method of "color(blue)"completing the square"#

#• " ensure the coefficient of "x^2" term is 1"#

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

#rArry=-12x^2+6x-18#

#color(white)(rArry)=-12(x^2-1/2x+3/2)#

#color(white)(rArry)=-12(x^2+2(-1/4)xcolor(red)(+1/16)color(red)(-1/16)+3/2)#

#color(white)(rArry)=-12(x-1/4)^2-69/4larr" in vertex form"#

#"with " h=1/4" and "k=-69/4#

#rArrcolor(magenta)"vertex "=(1/4,-69/4)#