Graphing Calculator: Plot Functions, Roots & Intersections

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Formula at a glance

Graphing Calculator: Roots — f(x) = 0. Example: Parabola and sine wave → y = x² − 2: x-intercepts: −1.41421, 1.41421 · y-intercept: −2 — How the Graphing Calculator works: Roots — f(x) = 0

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📘 About the Graphing Calculator

A graph shows at a glance how a function behaves — where it is positive, where it crosses the axes, where it peaks and how fast it grows. Plotting two functions together shows where they are equal, which solves the equation f(x) = g(x).

Type up to three functions and the x-range. The calculator plots them and lists the x-intercepts (roots), the y-intercept, local maxima and minima (where the derivative is 0) and the intersection points of each pair, so you can solve equations graphically.

🧮 Formula

Roots

f(x) = 0

Turning points

f′(x) = 0; minimum if f″ > 0, maximum if f″ < 0

Intersections

f(x) = g(x)

✏️ Worked examples

Parabola and sine wave

You enter
y₁ =	x^2 - 2
y₂ = (optional)	sin(x)
x from	-10
x to	10
Trig functions use	Radians

You get
y = x² − 2	x-intercepts: −1.41421, 1.41421 · y-intercept: −2
y = sin(x)	x-intercepts: −9.42478, −6.28319, −3.14159, 0, 3.14159, 6.28319, 9.42478 · y-intercept: 0

x-intercepts: −1.41421, 1.41421 · y-intercept: −2.

Cubic with turning points

You enter
y₁ =	x^3 - 3x
x from	-3
x to	3
Trig functions use	Radians

You get
y = x³ − 3x	x-intercepts: −1.73205, 0, 1.73205 · y-intercept: 0

x-intercepts: −1.73205, 0, 1.73205 · y-intercept: 0.

🧭 How to use this calculator

What you enter

y₁ =
y₂ = (optional)
y₃ = (optional)
x from
x to
Trig functions use

What you get

y = x² − 2
y = sin(x)

❓ Frequently asked questions

How do I type functions?

Use ^ for powers (x^2), * or juxtaposition for multiplication (2x, 3sin(x)), and functions with brackets: sqrt(x), ln(x), log(x), e^x, abs(x).

How do I find where two graphs intersect?

Enter both functions — the intersection points are listed below the graph.

Why does the graph look cut off near an asymptote?

Very large values (like 1/x near 0) are clipped so the rest of the graph stays readable.

📉 Graphing Calculator: Plot Functions Online