Quadratic and polynomial functions worksheets Grades 10–11

Vertex form, the discriminant, complex roots, polynomial and synthetic division, and the remainder, factor and rational root theorems.

Vertex form of a quadraticComplete the square to write y = a(x − h)² + k and name the vertex.
Finding the vertex from standard formFind the vertex with x = −b ÷ 2a, then find y.
The discriminantUse b² − 4ac to tell how many real roots a quadratic has.
Quadratic equations with complex rootsSolve quadratics whose roots are complex numbers with the quadratic formula.
Polynomial long divisionDivide polynomials with long division and write the quotient and remainder.
Synthetic divisionDivide a polynomial by x − c with synthetic division.
The remainder theoremFind the remainder of P(x) ÷ (x − c) by working out P(c).
The factor theoremShow x − c is a factor, divide it out, and factor what is left.
The rational root theoremList the possible rational roots, find one that works, divide and factor.

Unit packet

One two-sided worksheet for every topic, then the unit test, with the answer key at the back. Fresh each time.

Two problems from every topic. Pass it and move up to the next unit.