<Midterm Review>

Ch.1 Roots and Powers

  • Natural Numbers
  • Whole Numbers
  • Integers
  • Rational Numbers
  • Irrational Numbers

n is the index

a is the radicand

n√ is the root symbol

n√a is the radical

Ex)

 

Ch.2 Radical Operations and Equations

Recall the multiplication property of radicals

n√ab =n√a x n√b, where n ∈ N and a,b, n√a, n√b ∈ R

This property is used to  write radicals in different forms. In the same way that 3 is the coefficient of the algebric term, 3x, we say that 3 is the coefficient of the mixed radical, 3√7.

Ch.3 Solving Quadratic Equations

Factoring

1 – one thing in common GCF a (b+c)

2 – two terms -> difference of squares (a+b)(a+b)

3- three terms -> pattern x^ x # product and sum

ex)

Ch.4 Analyzing quadratic Functions and Inequalities

  1. units left – y=(x+2)^2
  2. Units right –y=(x-2)^2
  3. units up – y=x^2 +2
  4. units down – y=x^2 - 2

standard Form

y=a(x-p)^2+q

vertex = (p,q)

axis of symmetry = x=p

ex) 2x^2 +5s-4= minimum value

-6x^2 +4x+3 = maximum value

Congruent = y=ax^2

 

*standard Form- y=a(x-p)^2+q

general Form – y=ax^2 +bx+c

Factored Form – y=(x-x1)(x+x2)