Change a number, change the shape. You're in charge.
A coefficient is a number that multiplies a variable. In y = 3x + 2, the 3 is a coefficient - it controls how steep the line is. Change it, and the whole graph changes.
Think of coefficients as control knobs on a graph. Each knob does something different: one controls steepness, another controls position, another controls shape. In this lesson, you'll learn what each knob does.
The simplest function family. Two coefficients, two controls: m for slope (steepness) and b for y-intercept (where it crosses the y-axis).
Drag the sliders to see how each coefficient controls the line. Use the ghost button to snapshot the current curve, then change a slider to see the difference.
Quadratics make parabolas - those U-shaped (or upside-down U) curves. Three coefficients, three controls: a for stretch & direction, h for horizontal shift, k for vertical shift.
The vertex - the tip of the parabola - always sits at the point (h, k). The dashed line through the vertex is the axis of symmetry.
Standard form is the other common way to write a quadratic. Instead of seeing the vertex directly, you see three coefficients: a (same as vertex form - stretch & direction), b (the linear coefficient), and c (the y-intercept).
The vertex isn't obvious from this form, but you can find it: x = -b / (2a). The explorer below computes it live and shows the equivalent vertex form so you can compare.
Two mini-games to check what you learned. Match a hidden graph by adjusting coefficients, or solve a one-move challenge.