Graphing CalculatorONLINE PLOTTER

Graphing Calculator

Graphing CalculatorONLINE PLOTTER

FREE ONLINE GRAPHING CALCULATOR

Graphing CalculatorPlot it. Read it. Check it.

Graph a line, parabola, or trig curve. Compare up to three functions on one grid and check their values side by side.

Start plotting ↗
Use explicit multiplication, like 2*x. Separate functions with a semicolon. Trig inputs use radians.
Graph window

Table of values

START WITH AN EXAMPLE

What do you want to graph?

Line

Enter 2*x+1. The graph crosses the y-axis at 1 and rises 2 units for each step right.

Parabola

Enter x^2-4. Its vertex is (0, −4), and its x-intercepts are −2 and 2.

Trig curve

Enter sin(x). It repeats every 2π radians and ranges from −1 to 1.

FROM EQUATION TO ANSWER

How to use the graphing calculator

01 · Enter a function Try 2*x+1.
02 · Frame the graph Adjust the X and Y bounds.
03 · Check the output Compare values in the table.
  1. Enter an expression in x, such as sqrt(x) or y=x^2-4.
  2. Click Plot functions. Add up to three expressions separated by semicolons to compare their shapes.
  3. Use the grid to estimate intercepts and check those estimates by substitution.

Common questions

Which operations are supported?

Addition, subtraction, multiplication, division, powers, parentheses, pi, e, sin, cos, tan, sqrt, abs, ln, log and exp. Use log for base 10 and ln for natural logarithms.

Can I graph an equation like x² + y² = 9?

This tool plots explicit functions y=f(x). To sketch that circle, enter sqrt(9-x^2); -sqrt(9-x^2).

Why does the graph have gaps?

Some expressions have undefined values, such as 1/x at x=0. The plot also breaks curves at large jumps to avoid drawing through likely discontinuities.

WORKED EXAMPLES

Read the graph, then check the algebra

Find slope and intercepts

Plot 2*x+1. At x=0, y=1, so the y-intercept is (0,1). At y=0, solve 2x+1=0 to get x=−0.5. Use the points (0,1) and (1,3) to check the slope: (3−1)/(1−0)=2.

Find where two graphs meet

Plot x^2; 2*x+3. Intersections occur where the outputs agree. Solving x²=2x+3 gives (x−3)(x+1)=0. Substitution gives the two points (−1,1) and (3,9).

Distinguish a gap from a viewing limit

Plot 1/(x-2). At x=2 the denominator is zero, so there is no point on the curve. Plot sqrt(x-2) to see a different restriction: its real graph begins at (2,0) and continues right.

Set a graph window that shows the feature

If a graph appears empty, check whether its y-values are outside the window. For x^2+20, try x from −5 to 5 and y from 15 to 45. The vertex at (0,20) becomes visible. Press Plot functions after changing the bounds.

Use the table to check an estimate

The table samples nine evenly spaced x-values across the current window. An intercept or intersection can lie between rows, so check exact coordinates by substitution. The plotter accepts up to three explicit functions of x.

Graphing Calculator · Read the Graphing Guides

GRAPHING PRACTICE

Four experiments you can run right now

Use the Graphing Calculator to predict a result, plot it, and check it against a known point. Keep the original equation beside your graph so you can spot a mistyped sign or misplaced parenthesis.

01 · Move a parabola

Plot x^2; (x-3)^2+2. The first vertex is (0,0) and the second is (3,2). Compare the curves at x=3: the original gives 9 while the shifted curve gives 2. Both curves open upward and have the same shape. The horizontal shift comes from the expression inside the square, and the vertical shift comes from the constant outside it.

02 · Compare two slopes

Enter 2*x+1; -x+1. Both lines pass through (0,1), but one rises and the other falls as you move right. At x=2, the first line reaches 5 and the second reaches −1. To check that the lines meet only once, solve 2x+1=−x+1. This gives x=0, which matches the shared intercept.

03 · Find a hidden feature

Plot (x-12)^2+4. The vertex sits outside the default x-window. Change the x bounds to 8 and 16 and the y bounds to 0 and 22. The minimum appears at (12,4). Sample x=11 and x=13 in the values table. Both give 5, which confirms the symmetry around x=12.

04 · Check an undefined value

Enter 1/(x-2) and set x from −2 to 6. The table includes x=2, where the denominator is zero and the output is undefined. Values immediately to either side have opposite signs. The vertical asymptote describes the curve’s behavior near that x-value, even though the function has no value there.

Before comparing curves, pick an x-value that makes the arithmetic simple. Zero often reveals the y-intercept, while one can help check a coefficient or exponent. If two expressions agree at one sampled point, test another input before treating them as equivalent. Different functions can share several points.

When the plot looks wrong

Start with the input. Type 2*x for multiplication and use parentheses to group a denominator, as in 1/(x-2). For trigonometric functions, enter angles in radians. Compare sin(pi/2), which equals 1, with sin(90), where 90 is interpreted as radians.

Then check the window. A line or curve can sit outside the visible area even when the expression is valid. Try bounds that include the point you expect to see. If the feature looks crowded, tighten the bounds around it and plot again.

The Graphing Calculator draws sampled curves, so use algebra to confirm exact roots, turning points and intersections. A value table helps you test specific inputs and distinguish a genuine gap from a feature outside the view.

GRAPHING GUIDES

Learn one graph at a time

How to Graph a Linear Equation

Graph a linear equation from slope-intercept or standard form. Follow worked examples and check your line using two points.

Conclusion

Use the Graphing Calculator to plot an equation, adjust the viewing window, and check what you see against the values table. If you need an exact intercept or intersection, verify it algebraically. Start with a familiar function, then change one term to see how the curve responds.

Try an equation in the calculator ↑