Graphing Calculator
A graph turns an equation into a picture, showing where a function rises, falls and crosses the axes. Type a function of x, choose the range and this calculator draws it, marks where it crosses the x-axis and reports the y-intercept and the lowest and highest values in your window. It supports powers, roots, absolute value, logarithms and trigonometric functions.
How to use the graphing calculator
- Type a function using x, for example x^2 - 4 or sin(x). You can write “y = …” too.
- Set the x range you want to see.
- Read the graph, the roots (where the curve crosses y = 0) and the minimum and maximum.
Formula
The calculator evaluates f(x) at 300 evenly spaced points and joins them. Roots are found where the sign of f changes, refined by repeated halving (bisection). Use ^ for powers, sqrt(), abs(), ln(), log(), sin(), cos(), tan(), pi and e. Trig functions use radians.
Worked examples
A parabola
f(x) = x² − 4 has roots at −2 and 2, a y-intercept of −4 and a minimum of −4 at x = 0.
A line
f(x) = 2x + 1 crosses the x-axis at −0.5 and the y-axis at 1.
A wave
f(x) = sin(x) crosses zero at 0, π ≈ 3.14 and 2π ≈ 6.28, and stays between −1 and 1.
Reading a graph
Key features to look for
| Feature | What it means |
|---|---|
| x-intercepts (roots) | Where f(x) = 0 |
| y-intercept | The value f(0) |
| Turning points | Local minimum or maximum |
| Asymptote | A line the curve approaches but does not reach |
Common function shapes
- Linear (mx + b): a straight line with slope m.
- Quadratic (ax² + bx + c): a parabola opening up if a > 0.
- Cubic: an S-shape with up to two turning points.
- sin and cos: waves repeating every 2π.
- 1/x: a hyperbola with an asymptote at x = 0.
Transformations
Adding a number to f(x) shifts the graph up; adding inside, f(x − 2), shifts it right; multiplying by −1 flips it over the x-axis. Try x^2, then (x-2)^2, then (x-2)^2 + 3 to see each shift.
Choosing a good window
If you cannot see the interesting part, change the range. A too-wide window flattens curves; a too-narrow one hides roots. See also the quadratic solver for exact roots.
Practice problems
Try these yourself first, then check your answer. The answers come from the calculator above.
- Find the roots of f(x) = x² − 6x + 8.
Show answer
Function: f(x) = x^2 - 6x + 8
- Where does f(x) = 3x − 9 cross the x-axis?
Show answer
Function: f(x) = 3x - 9
Common mistakes to avoid
- Forgetting that trig functions expect radians here.
- Choosing a range that hides the interesting part of the graph. Try zooming in or out.
- Leaving out multiplication in ambiguous places. 2x works, but write 2*(x+1) for clarity.
Frequently asked questions
How do I graph a function?
Type the function of x, set the range and the graph is drawn instantly.
What is a root?
A value of x where f(x) = 0, meaning the graph crosses the x-axis.
Why is there a gap in the graph?
The function may be undefined there, such as 1/x at x = 0.
Can I graph more than one function?
This tool plots one function at a time. To compare, use the range and check values by eye or with the equation solver.
Reviewed September 26, 2026 by the SolveCalcPro editorial team. Found a mistake? Tell us; see our editorial policy.