Vertex Form Calculator
Convert a quadratic between standard form (ax² + bx + c) and vertex form (a(x - h)² + k) instantly, in either direction.
ax² + bx + c
Vertex form
(x - 2)² - 1
Vertex (h, k)
(2, -1)
Recommended Settings
Pro Tips
- •The vertex (h, k) directly tells you the parabola's turning point - its maximum if a is negative, or minimum if a is positive
- •h is computed as -b/(2a), the x-coordinate of the axis of symmetry, and k is the function's value at that x-coordinate
- •Vertex form makes graphing much easier since you can immediately plot the vertex and know the direction of opening from the sign of a
- •Converting from vertex back to standard form is just expanding a(x-h)² + k algebraically - useful for finding a quadratic's roots via the quadratic formula
Most Popular
Most students convert standard form to vertex form to quickly find a parabola's minimum or maximum point
When to Use This Tool
Convert to vertex form to immediately read off the parabola's minimum or maximum point.
Switch between standard and vertex form for a homework problem that requires a specific format.
Use vertex form to plot a parabola quickly, starting from its turning point.
Verify a manually completed-the-square conversion between quadratic forms.
How It Works
For standard-to-vertex: compute h = -b/(2a) and k = c - b²/(4a), the coordinates of the parabola's vertex
For vertex-to-standard: expand a(x-h)² + k algebraically to recover the standard coefficients a, b, and c
Display the converted expression along with the vertex coordinates
100% Private
Files never leave your device. All processing happens locally in your browser.
Lightning Fast
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Open Source
Built with verified, open-source libraries. Fully transparent.
Frequently Asked Questions
What is the vertex of a parabola?
The vertex is the parabola's turning point - its minimum value if the parabola opens upward (a > 0), or its maximum value if it opens downward (a < 0).
How is h calculated?
h = -b / (2a), which is the x-coordinate of the parabola's axis of symmetry - the vertical line the parabola is mirrored around.
Why can't a be zero?
If a were zero, the equation would no longer be quadratic (it would be linear), so it wouldn't have a parabola or a vertex to convert.
Is my data sent anywhere?
No. All calculations happen locally in your browser.