1. **State the problem:** Find the y-intercept and x-intercepts of the function $$g(x) = -(x+5)^2 + 8$$ and describe the graph shape. 2. **Y-intercept:** The y-intercept occurs when $$x=0$$. Substitute $$x=0$$ into the function: $$g(0) = -(0+5)^2 + 8 = -25 + 8 = -17$$ So, the y-intercept is $$-17$$. 3. **X-intercepts:** The x-intercepts occur when $$g(x) = 0$$. Set the function equal to zero: $$0 = -(x+5)^2 + 8$$ Rearrange: $$-(x+5)^2 = -8$$ Multiply both sides by $$-1$$: $$\cancel{-}(x+5)^2 = \cancel{-}(-8)$$ $$(x+5)^2 = 8$$ Take the square root of both sides: $$x+5 = \pm \sqrt{8} = \pm 2\sqrt{2}$$ Solve for $$x$$: $$x = -5 \pm 2\sqrt{2}$$ 4. **Graph shape:** The function is a downward-opening parabola because of the negative sign in front of the squared term. The vertex is at $$(-5, 8)$$, which is the maximum point. **Final answers:** - Y-intercept: $$-17$$ - X-intercepts: $$-5 - 2\sqrt{2}, -5 + 2\sqrt{2}$$ - Graph shape: downward-opening parabola with vertex at $$(-5, 8)$$.