Example 1: x^2 + 6x + 5
Coefficient 'a': 1; Coefficient 'b': 6; Coefficient 'c': 5
a (Coefficient in vertex form): 1; k (y-coordinate of the vertex): -4; h (x-coordinate of the vertex): -3; k (Vertex form): -4; h (Vertex form): -3
Completing the Square Calculator
Math0.0(0)
Converts a quadratic expression to vertex form by completing the square.
More tools:Math & Statistics Calculators
How To Use
How to use this calculator
Start with your values, or try a preset.
Step 1
Enter Coefficient 'a', Coefficient 'b', and Coefficient 'c' in the units shown.
Step 2
Read a (Coefficient in vertex form), k (y-coordinate of the vertex), h (x-coordinate of the vertex), k (Vertex form), and h (Vertex form) in the results panel. Results update as you change the inputs.
Step 3
Choose a preset to load an example, then adjust the values for your situation.
Worked Examples
Example calculations
See the inputs and their calculated results.
Example 2: x^2 - 4x + 4
Coefficient 'a': 1; Coefficient 'b': -4; Coefficient 'c': 4
a (Coefficient in vertex form): 1; k (y-coordinate of the vertex): 0; h (x-coordinate of the vertex): 2; k (Vertex form): 0; h (Vertex form): 2
Example 3: 2x^2 + 8x + 1
Coefficient 'a': 2; Coefficient 'b': 8; Coefficient 'c': 1
a (Coefficient in vertex form): 2; k (y-coordinate of the vertex): -7; h (x-coordinate of the vertex): -2; k (Vertex form): -7; h (Vertex form): -2
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