How do you find the vertex of #y=2(x+4)^2-7#?

2 Answers
Jim G.
May 4, 2017

#(-4,-7)#

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"#

#y=2(x+4)^2-7" is in this form"#

#"with " h=-4" and " k=-7#

#rArrcolor(magenta)"vertex " =(-4,-7)#

Douglas K.
May 4, 2017

The standard vertex form form is:

#y = a(x-h)+k" [1]"#

where #(h,k)# is the vertex

Explanation:

Change the given equation,

#y=2(x+4)^2-7#

into the form of equation [1] by changing the plus sign into two minus signs:

#y = 2(x--4)^2-7" [2]"#

Matching equation [2] with equation [1], we can see that the vertex is, #(-4,-7)#

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