Question

Identify the vertex and the axis of symmetry of the graph of the function.

Answer 1

C) vertex: (-2, -4);

axis of symmetry: x = - 2

Explanation:

`y=2(x+2)^2-4`

One of the many ways to finding the vertex of a parabolic equation is to use the formula:
`h=-(b)/(2a)` for the x-coordinate of the vertex, and
`k=f(-(b)/(2a) )` for the y-coordinate of the vertex.

However, since this equation is in vertex form, the simplest way to find the vertex would be by applying your knowledge of the vertex form of the parabola.

In this equation, we have the vertex form of a parabola:
`y=a(x-h)^2+k`, where
`(h, \ k)` are the vertex coordinates.

In
`y=2(x+2)^2-4`:

• h = -2
• k = -4

You may be wondering why h = -2 and not +2. This is because since the original vertex form is (x - h), this equation is basically subtracting a negative 2 to create a positive 2.

Now that we have the h and k values, we know the vertex:

• 
  `(h, \ k)`

• 
  `(-2, \ -4)`

The axis of symmetry is the vertical line that cuts right through the center point of the parabola, aka the vertex. Therefore, the axis of symmetry would be found by:
`x=h`

For this particular equation, h = -2, so the axis of symmetry would be:

• 
  `x=-2`

This answer corresponds with Answer Choice C.