Interactive function grapher
Pick a function family and drag the sliders. The graph redraws live and the key features (intercepts, vertex, asymptotes, amplitude and period) are computed straight from the equation as you go, so the numbers always match the curve. Code-drawn, printable, free, no sign-up.
Equation
y = 1x² + 0x - 4
General form: y = ax² + bx + c
Key features (live)
- Opens
- upward
- Vertex
- (0, -4)
- Axis of symmetry
- x = 0
- y-intercept
- (0, -4)
- x-intercept(s)
- (-2, 0), (2, 0)
How to read each family
Linear lines change steepness with the slope m and slide up or down with the intercept b; the x-intercept is where the line crosses zero, at x = -b/m. Quadratic parabolas open upward when a is positive and downward when it is negative, with the vertex at x = -b/(2a) and up to two x-intercepts from the discriminant.
Exponential curves grow when the base is above 1 and decay when it is below 1, always crossing the y-axis at (0, a) and flattening toward the horizontal asymptote y = 0. Logarithmic curves are the mirror image: a vertical asymptote at x = 0, an x-intercept at (1, 0), and a domain of x > 0. Sine and cosine waves have amplitude |a|, period 2π/|b|, a phase shift of -c/b and a midline at y = d.
Explore alongside these lessons
This tool pairs with the algebra and functions worksheets and teaching units across the site. Use it to check an answer-key graph, to demonstrate how a single parameter changes a curve, or to let students discover a rule for themselves before you name it. Browse the worksheet library or the full set of free tools.
Questions
- What functions can I graph?
- Five families: linear (y = mx + b), quadratic (y = ax² + bx + c), exponential (y = a·bˣ), logarithmic (y = a·log_b(x)) and sine/cosine (y = a·sin(bx + c) + d). Each has sliders for its parameters, and the graph redraws instantly as you move them.
- Where do the key features come from?
- They are computed live from the current slider values, never stored or looked up. Move a slider and the vertex, intercepts, asymptotes, amplitude and period all recompute from the actual equation, so the numbers always match the curve on screen.
- How is the vertex of a parabola found?
- For y = ax² + bx + c the axis of symmetry is x = -b/(2a); substituting that back in gives the vertex y-value. The x-intercepts come from the discriminant b² - 4ac: two if it is positive, one if zero, none if negative.
- Why does the exponential curve never touch the x-axis?
- y = a·bˣ approaches but never reaches zero, so y = 0 is a horizontal asymptote. Because b⁰ = 1, the curve always crosses the y-axis at (0, a).
- Is it free?
- Yes. It runs entirely in your browser, with no login, no watermark and no daily limit. Nothing is sent to a server.