Quadratic Functions & Graphs

Once you can solve a quadratic, the next step is reading its graph — a parabola. Three features carry most of the questions:

• Zeros (the $x$-intercepts) — where the parabola crosses the $x$-axis. Set each factor equal to $0$; a product is zero only when a factor is.
• The vertex — the turning point, and the minimum or maximum value. Rewrite in vertex form $f(x) = a(x - h)^2 + k$ by completing the square, and the vertex is $(h, k)$.
• Meaning in context — for a height-vs-time model, the constant term is the initial height and a positive zero is when it lands.

These are real, released Regents questions; read each carefully.