What is the vertex form of #y= 12x^2-14x-6 #?

1 Answer
Jim G.
Apr 8, 2017

#y=12(x-7/12)^2-121/12#

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 constant.

#"Rearrange " y=12x^2-14x-6" into this form"#

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

#y=12(x^2-7/6x-1/2)larr" coefficient of " x^2" is unity"#

#y=12[(x^2-7/6xcolor(red)(+49/144))color(red)(-49/144)-1/2]#

#color(white)(y)=12[(x-7/12)^2-121/144]#

#rArry=12(x-7/12)^2-121/12larrcolor(red)" in vertex form"#

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