## Category: Pre-Calculus

- Basic Graphs of a Parabola
- Learn about graphs that occur throughout analytic geometry and calculus. The student should be able to recognize them -- and sketch them -- purely from their shape.
- Completing the Square
- Learn about the technique called completing the square. This means to make the quadratic into a perfect square trinomial, i.e. the form a² + 2ab + b² = (a + b)².
- Factorials
- Learn about factorials here.
- Functions
- When one thing depends on another, as, for example, the area of a circle depends on the radius, or the temperature on the mountain depends on the height, then we say that the first is a "function" of the other.
- Introduction to Graphs of Functions
- Learn about graphs of functions here.
- Inverse Functions
- Learn about the inverse of a function and how it undoes the action of that function.
- Linear Functions: The Equation of a Straight Line
- Covers the study of the graphs of polynomial functions. Observe that the graph of each degree leaves its characteristic signature on the x- y-plane.
- Logarithmic and Exponential Functions
- Learn about logarithmic and exponential functions.
- Logarithms
- A logarithm is the exponent to which the base must be raised to produce a given number.
- Mathematical Induction
- Mathematical induction is a technique for proving a statement -- a theorem, or a formula -- that is asserted about every natural number.
- Multiple Roots: Point of Inflection
- Learn about the graphs of polynomials that have multiple roots.
- Permutations and Combinations
- Learn about permutations, factorial representation of permutations, permutation problems, combinations, factorial representation of combinations, and combination problems,
- Quadratics: Polynomials of the Second Degree
- Quadratic is another name for a polynomial of the 2nd degree.
- Rational and Irrational Numbers
- Learn what a rational number is, which numbers have square roots, and more.
- Rational Functions
- Learn about rational functions, which are quotients of polynomials.
- Reflections of a Graph
- Consider the first quadrant point (a, b), and let us reflect it about the y-axis. It is reflected to the second quadrant point (-a, b).
- Roots of Polynomials of Degree Greater than 2
- Learn how to find the roots of a polynomial of degree greater than 2.
- Symmetry of a Graph
- A reflection through the origin is equivalent to a reflection about the y-axis, followed by a reflection about the x-axis.
- Synthetic Division by x-a
- Learn about the remainder theorem and the factor theorem.
- The Binomial Theorem
- The solution to the problem of the binomial coefficients without actually multiplying out, is called the binomial theorem. It gives the coefficients for the expansion of (a + b)n.
- The Roots or Zeroes of a Polynomial
- Learn about the polynomial equation, the roots, or zeros, of a polynomial, the x- and y-intercepts, and more.
- The Slope of a Straight Line
- Learn about the difference between a straight line, and a slope of a straight line.
- Topics in Precalculus
- Covers rational and irrational numbers, logarithms, graphs, and functions.
- Translations of a Graph
- A translation of a graph is its rigid movement, vertically or horizontally.
- Vocabulary of Polynomial Functions
- Functions can be categorized, and the simplest type is a polynomial function.