Vertex Form Calculator
Enter a, b, and c below to instantly convert ax² + bx + c into vertex form.
For ax² + bx + c
Vertex Form
2(x + 2)² − 5
Vertex: (-2, -5)
Converting to Vertex Form
h = −b / (2a). k = c − b² / (4a). These come directly from completing the square on ax² + bx + c.
Worked example
Convert 2x² + 8x + 3 to vertex form.
h = −8 / (2·2) = −2
k = 3 − 64 / (4·2) = 3 − 8 = −5
Vertex form: 2(x + 2)² − 5
Frequently Asked Questions
What is vertex form?
Vertex form writes a quadratic as a(x − h)² + k, where (h, k) is the parabola's vertex — its highest or lowest point.
How do you convert standard form to vertex form?
h = −b / (2a), and k = c − b² / (4a). This process is really just completing the square, done through a shortcut formula instead of writing out every algebra step.
How do you read the vertex from vertex form?
Directly: the vertex is (h, k). Watch the sign inside the parentheses — a(x − h)² + k has vertex (h, k), so a(x + 3)² + k means h = −3, not 3.
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