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

1 Answer
Sep 11, 2017

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 :)