What is the axis of symmetry and vertex for the graph y=x^2-4?

1 Answer
Parabola
Dec 15, 2017

This function is symmetric in respect to the y axis.
The vertex is (0,-4)

Explanation:

We can define a function as odd,even, or neither when testing for its symmetry.
If a function is odd, then the function is symmetric in respect to the origin.
If a function is even, then the function is symmetric in respect to the y axis.
A function is odd if -f(x)=f(-x)
A function is even if f(-x)=f(x)

We try each case.
If x^2-4=f(x), then x^2-4=f(-x), and -x^2+4=-f(x)

Since f(x) and f(-x) are equal, we know this function is even.

Therefore, this function is symmetric in respect to the y axis.

To find the vertex, we first try to see what form this function is in.

We see that this is in the form y=a(x-h)^2+k

Therefore, we know that the vertex is (0,-4)

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