AI Graphing Solver
A graph turns an equation into a picture you can read. Enter y = x² − 4 in this AI graphing solver and the curve is drawn on a coordinate grid, so you can spot where it crosses the axes and how it behaves.
How to plot a function
Type a function of x, with or without “y =”, and press Solve. The curve is drawn on a grid from −10 to 10 on both axes. Use ^ for powers, / for division and brackets to group terms. Useful forms include y = 2x − 3, y = x^2 − 2x − 3, y = 1/(x − 2) and y = sin(x).
What to read from a graph
- y-intercept: where the curve crosses the y-axis, found by setting x = 0.
- x-intercepts (roots): where it crosses the x-axis, found by setting y = 0.
- Turning points: the peak or valley of a curve, found with the derivative.
- Asymptotes: lines the curve approaches but never touches.
- Symmetry: parabolas are symmetrical about the vertical line through their vertex.
Graph shapes you will meet
| Equation form | Shape | Key feature |
|---|---|---|
| y = mx + c | Straight line | Slope m, y-intercept c |
| y = ax² + bx + c | Parabola | Opens up if a > 0, down if a < 0 |
| y = 1/x | Hyperbola | Asymptotes at both axes |
| y = sin x | Wave | Repeats every 360° or 2π |
To find turning points exactly, use the calculus solver; for exact roots of a parabola, use the quadratic equation solver.
Worked examples
Example 1: Graph y = x² − 4
- It is a quadratic with a = 1 > 0, so the parabola opens upwards.
- y-intercept: x = 0 gives y = −4.
- x-intercepts: x² = 4, so x = ±2.
- Vertex: the lowest point is (0, −4).
Final answer: Intercepts (−2, 0), (2, 0), (0, −4)
Example 2: Graph y = 2x − 3
- The slope is 2, so the line rises 2 for every 1 step right.
- y-intercept: (0, −3).
- x-intercept: set y = 0, so 2x = 3 and x = 1.5.
Final answer: Line through (0, −3) and (1.5, 0)
Example 3: Graph y = x² − 2x − 3
- Factor: (x − 3)(x + 1), so the roots are x = 3 and x = −1.
- Vertex x-coordinate: halfway between the roots, x = 1.
- Vertex y: 1 − 2 − 3 = −4.
Final answer: Vertex (1, −4); roots −1 and 3
Example 4: Graph y = 1/(x − 2)
- The denominator is zero when x = 2, so there is a vertical asymptote at x = 2.
- As x becomes very large, y approaches 0, so y = 0 is a horizontal asymptote.
Final answer: Asymptotes x = 2 and y = 0
Common mistakes to avoid
- Plotting only a few points and joining them with straight lines; curves need more points.
- Swapping the coordinates, writing (y, x) instead of (x, y).
- Reading the vertex of a parabola from the wrong side of the roots.
- Forgetting brackets: 1/(x − 2) is not the same as 1/x − 2.
- Ignoring the plotting window; features outside −10 to 10 will not appear.
Frequently asked questions
What range does the graph show?
The grid shows x and y from −10 to 10. Values outside that window are clipped.
Can I graph more than one function?
Plot one function at a time. Run another and compare the shapes.
How do I enter powers and roots?
Use ^ for powers, for example x^3, and sqrt(x) for square roots.
Can it plot trigonometric graphs?
Yes. Enter sin(x), cos(x) or tan(x). The x-values are treated as radians when plotting.
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AI-generated solutions are for learning purposes. Always verify important answers.