QUADRATICS MIND MAP

QUADRATICS MIND MAP

1. Expand & Simplify

   • Special Products
     • Squaring Binomials
       • (a+b)^2 = a^2+2ab+b^2
       • (a-b)^2=a^2+2ab+b^2
     • Product Sum/Difference
       • (a+b)=a^2+b^2
   • Multiplying Binomials
     • F.O.I.L
       • First
       • Outside
       • Inside
       • Last

2. Factoring

   • Polynomials
     • Greatest Common Factor
       • 2 Terms
         • Difference Squares
           • a^2-b^2=(a+b)(a-b)
       • 3 Terms
         • Simple Trinomial
           • Product Sum
         • Complex Trinomial
           • Criss-Cross Method
           • Decomposition Method
         • Perfect Square Trinomial
           • (a+b)^2=a^2+2ab+b^2
           • (a-b)^2=a^2-2ab+b^2
       • 4 Terms
         • Grouping

3. Complete the Squares

   • Standard Form to Vertex Form
     • Factor
     • Magic Number
     • Add & Subtract Magic Number
     • Remove 4th Term from Brackets
     • Factor to Solve

4. Factored Form

   • Set to 0 for x-intercepts
   • y=a(x-r)(x-s)
   • X-intercepts
     • "r"
     • "s"

5. Graphing

   • ax^2+bx+c
     • Factor to Factored Form [y=a(x-r)(x-s)]
   • Solve for x-intercepts
   • AOS=r+s/2

6. Quadratic Equations

   • Quadratic Formula
     • Solve for x
     • x=-b+/-√b^2-4ac/2a
       • No Solution
       • Two Solutions
       • One Solution
   • ax^2+bx+c
   • X-coordinate of Vertex
     • -b/2a
   • Equation of AOS
     • x=-b/2a

7. Standard Form

   • y=ax^2+bx+c
     • Parabola
     • Vertex
     • Axis of Symmetry
     • Finite Differences
       • Linear
       • Quadratic
       • Neither

8. Transformations

   • y=a(x-h)^2+K
     • Properties
       • Vertex = (h,K)
       • AOS = X
       • Direction of Opening
         • a=+ (up)
         • a=-(down)
       • Value of x
         • Any Real Number
       • Value of y
         • y > 0
   • "a"
     • Opening Up/Down Parabola
     • Vertically Stretched/Compressed
   • "h"
     • Horizontal Transformation
   • "K"
     • Vertical Transformation