How to Locate the Focus of a Parabolic Umbrella
- 1). Identify "h", "k" and "p" from the parabola equation. All parabolas can be written in the form 4p(y-k) = (x-h)^2. The "x" and "y" represent the x and y axis in the standard coordinate graphing plane.The "h" and "k" represent the vertex or center of the parabola, and "p" represents the distance from the vertex to the focus. If you have the parabola x^2-x+7, for example, then h = -2, k = 1 and p = 2.
- 2). Plug the numbers for "h", "k" and "p" into the focus formula, (h, k+p). The "h", "k" and "p" from Step 1 yield (-2, 1+2), which simplifies to give you a focus of (-2, 3).
- 3). Check the focus you found by graphing the parabola and the focus. The focus will be right above the exact center of the parabolic U. If the focus you found is off-center or located outside the U shape, then double-check your numbers.
