math ToolUpdated 2026-09-20
Graphing Calculator & Function Solver
Analyze algebraic functions and curves online. Enter polynomial coefficients to calculate function roots (x-intercepts), vertex coordinates, and plot curve data points across any interval.
Formula & Mathematical Methodology
f(x) = ax² + bx + c; Vertex x = -b ÷ 2a; Roots x = (-b ± √(b² - 4ac)) ÷ 2a
Analyzes parabolic and polynomial curves. Identifies roots where the function intersects the x-axis (f(x) = 0) and the extremum vertex where the slope of the tangent equals zero.
Step-by-Step Worked Example
Scenario: Plot f(x) = 1x² - 4x + 3
1. Calculate roots: (x - 1)(x - 3) = 0 → x₁ = 1, x₂ = 3.
2. Find vertex x-coordinate: x = -(-4) ÷ (2 × 1) = 2.
3. Find vertex y-coordinate: f(2) = (2)² - 4(2) + 3 = 4 - 8 + 3 = -1.
4. Vertex point: (2, -1) [Minimum].
Final Calculated Result: Roots at x = 1, 3; Vertex at (2, -1)
Frequently Asked Questions
Does this calculator support trigonometric graphs?
You can also analyze trigonometric functions such as sine, cosine, and tangent using our Scientific Calculator.
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