Question

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

Answer 1

`(-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)`

Answer 2

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)`