find the vertex and line of symmetry

f(x)=x^2-8x-6

To find the vertex and line of symmetry of a quadratic function, we can use the vertex formula. The quadratic function is in the form of f(x) = ax^2 + bx + c, so we can identify the values of a, b, and c to calculate the vertex.

In the given function f(x) = x^2 - 8x - 6, we have:
a = 1 (coefficient of x^2)
b = -8 (coefficient of x)
c = -6

The x-coordinate of the vertex (denoted as h) can be found using the formula h = -b / (2a). Plugging in the values, we have:
h = -(-8) / (2 * 1) = 8 / 2 = 4

To find the y-coordinate of the vertex (denoted as k), we substitute the value of h back into the original equation to get:
k = f(4) = 4^2 - 8(4) - 6 = 16 - 32 - 6 = -22

So the vertex of the function is (4, -22), where 4 is the x-coordinate (line of symmetry) and -22 is the y-coordinate of the vertex. Therefore, the line of symmetry is x = 4.