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What is the vertex form of #y= 3x^2-15x-14 #?

Answer 1

Eli Assouline

#y=3(x-5/2)^2-131/4#

#"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"#

#rArry=3(x^2-5x-14/3)#

#• " add/subtract "(1/2"coefficient of the x-term")^2" to"# #x^2-5x#

#y=3(x^2+2(-5/2)xcolor(red)(+25/4)color(red)(-25/4)-14/3)#

#color(white)(y)=3(x-5/2)^2+3(-25/4-14/3)#

#color(white)(y)=3(x-5/2)^2-131/4larrcolor(red)"in vertex form"#

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.