Focus is at (1,5) and directrix is y=7. So the distance between focus and directrix is 7−5=2units Vertex is at the mid point between Focus and Directrix. So vertex co-ordinate is (1,6) . The parabola opens down as focus is below the Vertex. We know the equation of parabola is y=a⋅(x−h)2+k where (h,k) is the vertex. Thus the Equation becomes y=a⋅(x−1)2+6 now a=14⋅cwhere c is the distance between vertex and directrix; which is here equal to 1 so a=−14⋅1=−14 (negative sign is as the parabola opens down) So the equation becomes y=−14⋅(x−1)2+6ory=−14⋅x2+12⋅x+236graph{-1/4x^2+1/2x+23/6 [-10, 10, -5, 5]} [ans]
