Test Review

(+) Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.

Solve quadratic equations with real coefficients that have complex solutions.

Factor a quadratic expression to reveal the zeros of the function it defines.

Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x - a is p(a), so p(a) = 0 if and only if (x - a) is a factor of p(x).

Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.

Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.

For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.*

Graph linear and quadratic functions and show intercepts, maxima, and minima.

Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.

Make sense of problems and persevere in solving them.

Reason abstractly and quantitatively.

Use appropriate tools strategically.

Attend to precision.