Find the equation of the axis of symmetry and the coordinates of the vertex of the graph of the following function. y=x^2-6x-4

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.