Question

Given `y=-2(x+4)^2-3`, how do you find the vertex and axis of symmetry?

Answer 1

`"vertex " =(-4,-3)," axis of symmetry is " x=-4`

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.

`y=-2(x+4)^2-3" is in this form"`

`" Note " (x+4)^2=(x-(-4))^2`

`"by comparison " h=-4" and " k=-3`

`rArr" vertex " =(-4 ,-3)`

The axis of symmetry passes through the vertex.

Since the coefficient of `(x+4)^2" is negative, then the parabola opens down"`

`rArr"equation of vertex is " x=-4`
graph{-2(x+4)^2-3 [-10, 10, -5, 5]}