Graphing Calculator
Plot any function of x, move sliders and read off roots, turning points and areas.
Examples: x^2 - 4, sin(x), a x^2 + b, (2, 3) for a point, x = 1 for a vertical line, x^2 {0 < x < 3} to limit x. Trig uses radians.
Key points
Key points are found in the part of the graph you can see. Zoom out to find more.
See it happen: Graph transformations
Formulas
- Straight line y = mx + c, with gradient m = (y₂ − y₁) / (x₂ − x₁)
- Turning point y = a(x − p)² + q has its turning point at (p, q)
- Area under a curve the integral of f(x) from a to b
Worked example
Find the roots, turning point and y-intercept of y = x² − 4x + 3.
- Type x^2 - 4x + 3. The curve crosses the x-axis at x = 1 and x = 3.
- Completing the square gives y = (x − 2)² − 1, so the turning point is (2, −1). It is a minimum because the x² term is positive.
- The y-intercept is the value at x = 0: y = 3.
Answer: Roots at x = 1 and x = 3, minimum at (2, −1), y-intercept 3.
Common mistakes
- Typing x2 or 2^x for x squared: powers need ^, so x squared is x^2.
- Reading a root from a zoomed-out graph: a root at 0.98 can look like 1, so use the listed values or zoom in.
- Counting an area below the x-axis as positive: the integral makes it negative, so split the region at the roots when you want the total area.
- Trying to plot x = 3 as y = ...: a vertical line is not a function of x.
About this tool
This graphing calculator plots as many functions of x as you like on the same axes. Letters such as a and b become sliders, so you can watch a curve change as a number changes. Under the graph it lists the roots, the y-intercept, the turning points and where the graphs meet, and each function can show its derivative, shade the area under it with the value worked out, and give a table of values to copy.
Tips
- The shaded area is signed: parts below the x-axis count as negative, as in an integral. Split it at the roots to get the total area.
- To solve f(x) = g(x), plot both and read where they meet.
- Trig uses radians: one full turn of sin(x) is 2π, about 6.28.
FAQ
- Is this graphing calculator free?
- Yes. It works in your browser with no account, and your graphs are kept on your device.
- How does it find the roots and turning points?
- It samples the curve across the visible part of the graph, then narrows each crossing or turn down by repeated halving, so the values are accurate to many decimal places. Zoom out to find points outside the view.
- How is the area worked out?
- By adaptive Simpson's rule, a numerical integration method. For ordinary school functions the answer is correct to the decimal places shown.