Visualize parabolas from coefficients and intervals. See vertex, intercepts, symmetry, and tables update live instantly. Ideal for algebra lessons, homework checks, revision, and exploration.
Sample quadratic: y = x2 - 4x + 3
| x | y |
|---|---|
| -1 | 8 |
| 0 | 3 |
| 1 | 0 |
| 2 | -1 |
| 3 | 0 |
| 4 | 3 |
| 5 | 8 |
The calculator uses the standard quadratic form:
y = ax2 + bx + c
Vertex x-coordinate: x = -b / (2a)
Vertex y-coordinate: substitute the vertex x-value into the function.
Discriminant: b2 - 4ac
Roots: x = (-b ± √(b2 - 4ac)) / 2a
Focus for a vertical parabola: (h, k + 1 / 4a)
Directrix for a vertical parabola: y = k - 1 / 4a
Enter the coefficients a, b, and c from your quadratic equation.
Set the minimum and maximum x-values to control the graph interval.
Choose how many points to generate for the coordinate table.
Enter any x-value in the evaluation field to compute f(x).
Pick the number of decimal places for rounded output.
Press Calculate Graph to show the summary, graph, and preview table above the form.
Use the export buttons to save the generated results.
A quadratic function creates a parabola. Its standard form is y = ax² + bx + c. The value of a controls width and opening. Positive a opens upward. Negative a opens downward. Larger absolute values make the curve narrower. Smaller absolute values make it wider. The value of b shifts the axis of symmetry. The value of c sets the y-intercept. These patterns help students read graphs faster and solve equations with confidence.
This calculator turns coefficients into a clear visual graph. It finds the vertex, discriminant, axis, roots, focus, and directrix. It also builds a coordinate table across your chosen interval. That table supports plotting by hand and checking homework. The graph shows how the parabola moves when coefficients change. This makes algebra lessons more practical. It also helps with exam review, tutoring, and classroom demonstrations.
The vertex is the turning point. The axis of symmetry passes through it. Real roots appear where the curve crosses the x-axis. When the discriminant is positive, there are two real roots. When it is zero, there is one repeated root. When it is negative, the graph has no real x-intercepts. The minimum or maximum value always occurs at the vertex. These features connect graphing and equation solving in one view.
Enter your coefficients and choose a helpful x-range. Then review the graph and generated table together. Compare the vertex with the roots and intercepts. Check whether the curve opens up or down. Use the export buttons to save results for reports or revision sheets. Repeat with different values to see transformations instantly. This repeated practice improves pattern recognition, strengthens algebra skills, and supports accurate graph interpretation.
Quadratic graphing appears in algebra, physics, business, and engineering. A fast visual check prevents sign mistakes and coefficient errors. Students can verify sketches before submitting work. Teachers can prepare examples quickly. Independent learners can test many cases in minutes. Because the table, graph, and summary update together, the relationship between symbolic form and geometric shape becomes easier to remember and explain clearly today.
Coefficient a controls the parabola’s opening and width. A positive value opens upward. A negative value opens downward. A larger absolute value makes the curve narrower.
The vertex is the turning point of the parabola. This calculator uses x = -b / (2a), then substitutes that x-value into the function to find y.
When the discriminant is negative, the quadratic has no real roots. The graph stays above or below the x-axis, so it never crosses it.
The axis of symmetry is the vertical line passing through the vertex. It divides the parabola into two matching halves and helps when sketching points.
Yes. You can enter integers, decimals, positive values, and negative values. Only a cannot be zero, because then the function is not quadratic.
Choose an interval wide enough to include the vertex and possible roots. If important features seem cut off, increase the minimum and maximum x-values.
The discriminant is b² - 4ac. It tells you whether the graph has two real roots, one repeated root, or no real roots.
Yes. It helps with checking manual graphs, confirming roots, studying transformations, and creating clean result tables for notes 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.