What is the vertex form of #y=2x^2 + 4x + 46 #?

1 Answer
Jim G.
Apr 3, 2017

#y=2(x+1)^2+44#

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 constant.

We can obtain vertex form by #color(blue)"completing the square"#

#y=2(x^2+2x+23)#

#color(white)(x)=2(x^2+2xcolor(red)(+1)color(red)(-1)+23)#

#color(white)(x)=2((x+1)^2+22)#

#rArry=2(x+1)^2+44larrcolor(red)" in vertex form"#

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