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What is the vertex form of #y=-4x^2-4x+1#?

Answer 1

Eva Abramson

The vertex form of equation is #y=-4(x+1/2)^2+2#

#y=-4x^2-4x+1# or

#y=-4(x^2+x)+1# or

#y=-4(x^2+x+1/4)+1+1# or

#y=-4(x+1/2)^2+2# . Comparing with vertex form of

equation #f(x) = a(x-h)^2+k ; (h,k)# being vertex we find

here #h=-1/2 , k=2 :.# Vertex is at #(-0.5,2) #

The vertex form of equation is #y=-4(x+1/2)^2+2#

graph{-4x^2-4x+1 [-10, 10, -5, 5]}

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Answer 2

Julia Adams

#y=-4(x+1/2)^2+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"#

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

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

#rArry=-4(x^2+x-1/4)#

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

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

#color(white)(rArry)=-4(x+1/2)^2-4(-1/4-1/4)#

#color(white)(rArry)=-4(x+1/2)^2+2larrcolor(red)"in vertex form"#

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Answer 3

Hazel Anglin

The vertex form of the quadratic equation ( y = -4x^2 - 4x + 1 ) is ( y = -4(x + 0.5)^2 + 3 ).

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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.