Quadratic Functions

A complete tutorial on \( f(x) = ax^2 + bx + c \): the vertex, axis of symmetry, discriminant, x-intercepts, and y-intercept, with worked examples.

A focused tutorial on \( f(x) = a(x - h)^2 + k \): maximum and minimum values, x- and y-intercepts, conversion to general form, and a live vertex-form applet.

Three methods — factored form, vertex form, and a linear system — plus a random-parabola practice applet.

Drag the coefficients \( a \), \( b \), and \( c \) and watch the parabola, vertex, and intercepts update in real time.

Visualize reflections, stretches, and absolute-value transformations of \( f(x) \), with both curves plotted side by side.

Seven worked problems on the vertex, x- and y-intercepts, and axis of symmetry — including three challenge problems on constrained vertices, transformations, and tangency.

Graded exercises on the vertex, intercepts, and discriminant, each with a full step-by-step solution.

The technique behind the vertex form — rewrite any quadratic in the form \( a(x - h)^2 + k \).

Why \( (ax + b)(Ax + B) \) is a quadratic, and how the factors' roots become the parabola's x-intercepts.

One long-form page combining the tutorial and the interactive grapher, with an FAQ at the end.