Question

Hi, Can you help me please? Thank you!

Identify the vertex and the axis of symmetry of the graph of the function `y = 2(x+2)^2 - 4`

A)
vertex: (-2, 4);

axis of symmetry: x = -2
B)

vertex: (2, -4);

axis of symmetry: x = 2
C)

vertex: (-2, -4);

axis of symmetry: x = -2
D)

vertex: (2, 4);

axis of symmetry: x = 2

Answer 1

Answer is (c).

Explanation:

Luckily, the equation was given to us in vertex form. This makes determining the vertex a lot easier.

In vertex form, the `h` and `c`/`k` value determines the vertex, where the `h` value is the `x` coordinate and the `c`/`k` value is the `y` coordinate.

Therefore, with an `h` value of `2`, we have to isolate that `2` in its respective bracket:

`x+2=0`

`x=-2`

This gives us `-2`. In relation to the graph, the function translates `2` units to the left; an `x` coordinate of `(-2, y)`.

As for the `y` coordinate, it's just the `c`/`k` value. So, `-4`.

Put this all together and our vertex is `(-2, -4)`.

---

The axis of symmetry is basically the `x` coordinate of the vertex, but an equation: `x=-2`.

If we graph the equation, we can confirm our vertex.

graph{y=2(x+2)^2-4 [-10, 10, -5, 5]}

Therefore, the correct answer is (c).

Hope this helps :)