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 :)