Vertex Form Calculator

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Choose whether to start from the standard form (a, b, c) or from the vertex form coefficients (a, h, k).
The leading coefficient. Must not be 0.
The linear coefficient.
The constant term. This is also the y-intercept (where the parabola crosses the y-axis).
Vertex formMinimum value y = -4
y = (x - 3)^2 - 4
Standard formy = x^2 - 6x + 5
Vertex x (h)3
Vertex y (k)-4
Axis of symmetryx = 3
y-intercept5
Discriminant (D)16
Root x11
Root x25
Root typeTwo real roots
OpensUpward (minimum at vertex)
Focus(3, -3.75)

The vertex is (3, -4), the lowest point of the parabola.

  • Because a = 1 > 0, the parabola opens upward and the vertex is its minimum.
  • The axis of symmetry is the vertical line x = 3, splitting the parabola into two mirror halves.
  • The y-intercept is 5, where the curve crosses the y-axis.
  • The discriminant D = 16 > 0, so the parabola has two real x-intercepts: x = 1 and x = 5.

Next stepUse vertex form in optimization problems: plug in the vertex y-value directly as the maximum or minimum, without solving.

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