Free lab

Function Graph Lab

Drag the coefficients to draw linear and quadratic functions, and read the roots, vertex, discriminant and sign intervals straight off the graph.

Quadratic function y = ax² + bx + c

Turn a down to 0 and the parabola collapses into a straight line. On the x-axis, a thick solid stretch means y > 0 and a dashed one means y < 0.

Try this: move only c — how does the parabola travel? When do the two roots merge into one, and what is Δ at that moment? Now move only b: what shape does the vertex trace out?

Linear function y = kx + m

Here b plays the role of the slope k, and c is the intercept m.

Try this: when the slope changes sign, which side of the root does the “positive half” move to? What happens when the slope is 0?

Fixed parabola, moving window

The parabola stays put while a window of width 3 slides along. When are the minimum ● and maximum ■ at the ends of the window, and when at the vertex?