1. The problem is to analyze and describe the graph of the function given by $$y = (x - 8)^2 - 6$$. 2. This is a quadratic function in vertex form: $$y = (x - h)^2 + k$$ where \(h = 8\) and \(k = -6\). 3. The vertex of the parabola is at the point \((8, -6)\). 4. Since the coefficient of the squared term is positive (1), the parabola opens upwards. 5. To find the y-intercept, set \(x = 0\): $$y = (0 - 8)^2 - 6 = 64 - 6 = 58$$ so the y-intercept is \((0, 58)\). 6. To find the x-intercepts, set \(y = 0\): $$0 = (x - 8)^2 - 6$$ $$ (x - 8)^2 = 6 $$ $$x - 8 = \pm \sqrt{6}$$ $$x = 8 \pm \sqrt{6}$$ So the x-intercepts are \(8 - \sqrt{6}\) and \(8 + \sqrt{6}\). 7. The axis of symmetry is the vertical line \(x = 8\). Final Answer: The parabola has vertex \((8, -6)\), opens upward, y-intercept \((0, 58)\), x-intercepts at \(8 \pm \sqrt{6}\), and axis of symmetry \(x = 8\).