Every thrown ball tells the same story: up, slowing, a breathless instant at the top, then down. That peak — the vertex — is the most important point on a parabola, and finding it is the whole reason the vertex form y = a(x − h)² + k exists: the vertex sits right there at (h, k), no algebra required. A quarterback's pass, a fountain's arc, the profit curve of a lemonade stand that peaks at the perfect price — wherever something rises then falls (or falls then rises), the vertex marks the maximum or minimum, the answer the problem was actually asking for.

From standard form y = ax² + bx + c, the vertex's x-coordinate is −b/(2a): the axis of symmetry, the line the parabola mirrors itself across. Plug that x back in to get the y. The sign of a tells you which way the story goes — negative a opens downward (a peak, like the ball), positive a opens upward (a valley, like a satellite dish). This calculator evaluates the vertex computation: enter your two known values and read the result. The classic application problem gives you a height function like h(t) = −16t² + 64t + 5 (feet, seconds) and asks when the ball peaks and how high — the vertex answers both at once.

With the pre-filled defaults — Variable A 10, Variable B 5 — the Parabola Vertex Calculator returns Result 50.0000. Change any input and those results update instantly, so you can see exactly how each number you enter moves the answer.