THIRD PARTIAL

THIRD PARTIAL

1. CUADRATIC INEQUALITIES

   • The area of the cut sections of a parabola
     • Depends on the direction of the parabola
       • Is a is positive and y > x, then the inner part applies
         • Is "a" is negative and y > x, then the outter part aplies

2. ROOTS OF A CUADRATIC EQUATION

   • -b/a = ALFA + BETA
   • c/a = ALFA x BETA

3. POLYNOMIALS

   • Y = A(n)X^n + A(n-1)X^(n-1).....A(0)X^0
   • THEOREMS
     • DESCARTES
       • In the function, The number of changes between positivesand negative terms is the maximum number of positive real solutions the function could have
         • APPLIES if A0 is different from 0
         • In the function when (-x) is applied, The number of chnges between positive and negative terms is the maximum number of negative real solution the function could have
     • REMEINDER
       • "The number which the polynmial is divided in a synthetic division and its remeinder, is a pont, (being the remeinder y) "
     • GENERAL THEOREM OF ALGEBRA
       • "The degree of a polynomial is the maximum number of solutions it can have"
     • TEST OF ZEROS
       • "The positive and negative division of the factors of An and A0, being A0 the numerator, are all the possible zeros"

4. INCREASING AND DECREASING FUNCTIONS

   • INCREASING: x1 < x2 then f(x1) < f(x2)
   • DECREASING: x1 < x2 then f(x1) > f(x2)