Exercise 12 Page 85

We want to write the equation of a parabola with vertex (2,6) and focus (2,2). Because the x-coordinate for the vertex and the focus is 2, the axis of symmetry of the parabola is the vertical line x=2. Equation:& y=1/4 p(x- h)^2+ k Vertex:& ( h, k) Focus:& ( h, k+ p) Since the vertex is ( 2, 6), we have that h= 2 and k= 6. Furthermore, we know that the y-coordinate of focus is 2. 2 = k+ p Let's substitute 6 for k in the above equation, and solve for p.

We can now write the equation of the parabola. y=1/4( - 4)(x- 2)^2+ 6 ⇔ y=-1/16(x-2)^2+6