Graph quadratic equations with vertex, roots, and symmetry details. Check values, inspect turning points, and export clear tables. Build confident parabola insights for every math practice.
Enter coefficients and graph settings below.
The graph updates after each calculation.
Sample equation used here: y = x² - 4x + 3
| x | y = x² - 4x + 3 |
|---|---|
| -2 | 15 |
| -1 | 8 |
| 0 | 3 |
| 1 | 0 |
| 2 | -1 |
The quadratic function uses the standard form y = ax² + bx + c.
Vertex x-coordinate: x = -b / 2a
Vertex y-coordinate: substitute vertex x into the function.
Discriminant: D = b² - 4ac
Roots: x = (-b ± √D) / 2a
Axis of symmetry: x = -b / 2a
The sign of a decides whether the parabola opens upward or downward.
It graphs any quadratic function written as y = ax² + bx + c. It also reports the vertex, roots, axis of symmetry, intercept, range, and opening direction.
If a equals zero, the equation becomes linear, not quadratic. A true parabola needs the x² term to remain present.
The discriminant shows how many real roots exist. A positive value gives two real roots. Zero gives one repeated root. A negative value gives no real roots.
The vertex is the turning point of the parabola. It is the minimum point when the graph opens upward and the maximum point when it opens downward.
The axis of symmetry is the vertical line passing through the vertex. The parabola mirrors itself on both sides of that line.
Changing the x-range helps you focus on useful parts of the parabola. A tighter range reveals detail, while a wider range shows overall shape and intercepts.
The CSV file contains every plotted x and y pair used to draw the graph. You can open it in spreadsheet software for further analysis.
Yes. It is useful for checking algebra steps, confirming graph features, preparing examples, and creating quick data tables for lessons or assignments.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.