Function Grapher & Equation Visualizer
Graph linear, quadratic, cubic, quartic and general functions; see roots, vertex, intercepts and intersections, derivative and tangent lines, and the area of a definite integral, with coefficient sliders
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Draws polynomials and other functions on a graph you can move and zoom, and lists roots, intercepts, turning points and intersections. Use it to check homework or to see how a coefficient changes a curve.
How to use
- Under "Coefficients", pick a degree from 1 to 4 and move the sliders, or type values in the boxes.
- For other functions, switch to "Type functions" and enter up to four, such as sin(x). Typing x^2 = x + 2 draws both sides and their solutions.
- Read the "Analysis": roots with double roots marked, the vertex or turning points, intervals and the factored form.
- Tick "Tangent line" or "Area of the definite integral" and drag the round handle or set x₀, a and b.
- Press "Save as image" for a PNG, or "Copy link" to share the graph.
How it works
- Polynomials use exact fractions: roots appear as fractions, square roots or a ± bi, and integrals come from the antiderivative. Roots found only approximately are marked numeric.
- Other functions are analysed numerically inside the visible range. log(x) is base 10, ln(x) is natural, angles are in radians.
Questions and answers
- How do I find the roots of a quadratic function from its graph?
- They are where the curve crosses the x-axis. y = x² − 4x + 3 crosses at x = 1 and x = 3.
- What does a double root look like on a graph?
- The curve touches the x-axis without crossing it, as y = x² − 2x + 1 does at x = 1.
- How do I find the equation of a tangent line?
- Its slope is f′(x₀), so the line is y = f′(x₀)(x − x₀) + f(x₀). Tick "Tangent line" to see it as y = mx + k.
- Why can a definite integral be smaller than the shaded area?
- Area below the x-axis counts as negative. For y = x² − 1 from −1 to 1 the integral is −4/3, but the area is 4/3.