Pre-calculus Contents E

f (x) = mx + c
Roots or zeros, x- and y-intercepts of a graph
Absolute value functions and equations
f (x) = | x |
The graph of absolute value of a linear function  f (x) = | ax+ b |
Linear equation with absolute value, graphic solution
Absolute value inequalities
Solving linear inequalities with absolute value
Equations of the straight line
Definition of the slope of a line
Slope-intercept form of a line
The point-slope form of a line
The two point form of the equation of a line
Parallel and perpendicular lines
Polynomial and/or Polynomial Functions and Equations
Definition of a polynomial or polynomial function
Division of polynomials

Factoring polynomials and solving polynomial equations by factoring
Solving quadratic and cubic equations by factoring examples
Polynomial functions
The source or the original polynomial function
Translating (parallel shifting) of the source polynomial function
Coordinates of translations and their role in the polynomial expression
Roots or zeros of polynomial function
Vieta's formulas
Graphing polynomial functions
Zero polynomial
Constant function
Linear function
Transition of the quadratic polynomial from the general to source form and vice versa
The zeros or the roots of the quadratic function
Vertex (the turning point, maximum or minimum) - coordinates of translations
Cubic function
Transformation of the cubic polynomial from the general to source form and vice versa
Coordinates of the point of inflection coincide with the coordinates of translations
The source cubic functions are odd functions
There are three types of the cubic functions - the classification criteria diagram
The graphs of the source cubic functions
Translated cubic functions
Translated cubic function, the type 1 - the tangent line at the point of inflection is horizontal
Translated cubic function, the type 2/1 - no turning points, the tangent at inflection is a slant line
Translated cubic function, the type 2/2 - with two turning points, the tangent at inflection is a slant line
Graphing a cubic function examples
Graphing translated cubic function type 2/2
Quartic function
Transformation of the quartic polynomial from the general to source form and vice versa
The coordinates of translations formulas
The values of the coefficients, a2 and a1 of the source quartic function y = a4x4 + a2x2 + a1x
The basic classification criteria diagram for quartic function
The graphs of quartic functions and their characteristic points
The quartic  type 1,   y - y0 = a4(x - x0)4a2 = 0 and a1 = 0
The quartic  type 2,   y - y0 = a4(x - x0)4 + a1(x - x0)a2 = 0
The quartic  type 3/1,   y - y0 = a4(x - x0)4 + a2(x - x0)2a1 = 0 and  a4a2 > 0
The quartic  type 3/2,   y - y0 = a4(x - x0)4 + a2(x - x0)2a1 = 0 and  a4a2 < 0
The graphs and classification criteria diagram for the quartics types 4/1 to 4/6,
y - y0 = a4(x - x0)4 + a2(x - x0)2 + a1(x - x0)
The zeros and the abscissas of the turning points of the source quartics types 4/1 to 4/6
Graphing the quartic polynomial, example
Pre-calculus Contents