By John Gugie — Updated Aug 30, 2022
A parabola is the classic U‑shaped curve that is symmetric around its vertex and intersects the x‑axis and y‑axis at distinct points. Its standard vertex form is y – k = a(x – h)².
Begin by writing the quadratic equation. If it isn’t already in vertex form, rearrange it to y – k = a(x – h)². For example: y – 3 = –⅙(x + 6)².
The vertex coordinates are (h, k). Extract h and k from the equation. In the example, h = –6 and k = 3, so the vertex is (–6, 3).
Set x = 0 and solve for y. For the example, y = –3, giving the point (0, –3).
Set y = 0 and solve for x. Taking the square root introduces ±, yielding two solutions: x = –6 ± √6, which are approximately –3.55 and –8.45.
Draw a blank coordinate plane on graph paper. Choose a scale that comfortably contains the vertex and intercepts, and extend the axes slightly beyond them to represent the parabola’s infinite arms. Mark equal tick marks along both axes.
Mark the vertex, the y‑intercept, and the two x‑intercepts with large dots. Connect these points with a smooth, continuous U‑shaped curve, extending the line toward the arrowheads on both axes to indicate the parabola’s endless reach.
Even with a calculator, double‑check every calculation to ensure accuracy.
