The coordinates of the vertex are (3, -13) and the axis of symmetry is at x = 3.
We can find the vertex by using the formula for finding x-coordinates. The formula for the x-coordinate of a vertex is below.
-b/2a
In this equation, a is the coefficient of the x^2 term (1) and b is the coefficient of the x term (-6). Then we can plug in to find the x term.
-(-6)/2(1)
6/2
3
Now that we have this term, we can plug it in for all values of x to find the y term.
x^2 - 6x - 4
3^2 - 6(3) - 4
9 - 18 - 4
-13
Now we know that the vertex is at (3, -13). Now finding the axis of symmetry is easy because the axis of symmetry in any quadratic is simply x = [x-coordinate of vertex]. So in this case it would be x = 3.
