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What is the vertex form of #y= (x+2) (2x+5) #?

Answer 1

Hazel Anglin

#y=2(x+9/4)^2-1/8#

#"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"#

#y=(x+2)(2x+5)larrcolor(blue)"expand the factors"#

#color(white)(y)=2x^2+9x+10#

#"to obtain vertex form use "color(blue)"completing the square"#

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

#rArry=2(x^2+9/2x+5)#

#• " add/subtract "(1/2"coefficient of the x-term")^2" to"# #x^2+9/2x#

#rArry=2(x^2+2(9/4)xcolor(red)(+81/16)color(red)(-81/16)+5)#

#color(white)(y)=2(x+9/4)^2+2(-81/16+5)#

#color(white)(y)=2(x+9/4)^2-1/8larrcolor(red)"in vertex form"#

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Answer 2

Savannah Anderson

The vertex form of the given quadratic equation y = (x + 2)(2x + 5) is y = 2(x + 1.25)^2 - 6.25.

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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.