Quadratic Relation

Nota:

• the graph of a quadratic relation is called a Parabola  It can either open up or down, depends on the second difference.

1. Equations

   Nota:

   • No-Frills equation(basic equation): y=x(square) Stretch Factor : - Determines the shape(the step pattern) of a parabola - Determines whether the parabola opens up (concave up) or down (concave down)
   1. Vertex Form y=a(x-h)(square) +k
      1. gives the stretch factor (a) and the vertex (h,k)

         Nota:

         • Vertex : the point on the graph with the least or greatest y-coordinate h is the x-coordinates of vertex, k is the y-coordinates of vertex
         1. If h>0 the curve is horizontally translated h units to right If h<0 the curve is horizontally translated h units to left If k>0 the curve is vertically translated k units up If k<0 the curve is vertically translated k units down
         2. If a>1 the curve is VERTICALLY STRETCHED by a factor of a If 0<a<1 the curve is VERTICALLY COMPRESSED by a factor of a. If a<0 the curve is reflected in the x-axis
   2. Factored Form y=a(x-s)(x-t)
      1. gives the stretch factor by a
   3. Standard Form y=ax+by+c
      1. gives the stretch factor and the y intercept(c)
      2. Factoring

         Nota:

         • Standard form became factored form through factoring Factoring: the process of expanding and simplifying done in reverse
   4. Transformation

      Nota:

      • begin with the No-Frills parabola: y=x(square) and add to it
      1. HORIZONTAL AND VERTICAL TRANSLATIONS
      3. VERTICAL STRETCHES,COMPRESSIONS & REFLECTIONS
   5. 3 forms of equation
2. can be identified by second differences that are constant
3. P.S. click on the top right corner of each box <-----