Question 395274
The x-coordinate of the vertex is given by:
{{{x = -b/2a}}} and here, a = 1 and b = -12,
{{{x = -(-12)/2(1)}}}
{{{x = 6}}} substitute into the given equation to find the y-coordinate of the vertex:
{{{y = x^2-12x-5}}}
{{{y = 6^2-12(6)-5}}}
{{{y = -41}}}
The vertex is at: (6, -41)
The equation of the line of symmetry is: x = 6
The vertex (6, -41) is a minimum because the parabola opens upwards (positive coefficient of {{{x^2}}}).
{{{graph(400,400,-5,20,-45,5,x^2-12x-5)}}}