Y = -(1/2)(x-2)² +8 Re write it in standard form: (y-8) = -1/2(x-2)² ↔ (y-k) = a(x-h)²
This parabola open downward (a = -1/2 <0), with a maximum shown in vertex The vertex is (h , k) → Vertex(2 , 8) focus(h, k +c ) a = 1/4c → -1/2 = 1/4c → c = -1/2, hence focus(2, 8-1/2) →focus(2,15/2)
Latus rectum: y-value = 15/2
Replace in the equation y with 15/2→→15/2 = -1/2(x-2)² + 8 Or -1/2(x-2)² +8 -15/2 = 0 Solving this quadratic equation gives x' = 3 and x" = 2, then Latus rectum = 5
