Quadratic Relation

Quadratic Relation

1. Equations

   • 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)
   • Vertex Form y=a(x-h)(square) +k
     • gives the stretch factor (a) and the vertex (h,k)
       • 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
       • 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
       • 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
   • Factored Form y=a(x-s)(x-t)
     • gives the stretch factor by a
   • Standard Form y=ax+by+c
     • gives the stretch factor and the y intercept(c)
     • Factoring
       • Standard form became factored form through factoring Factoring: the process of expanding and simplifying done in reverse
   • Transformation
     • begin with the No-Frills parabola: y=x(square) and add to it
     • HORIZONTAL AND VERTICAL TRANSLATIONS
     • VERTICAL STRETCHES,COMPRESSIONS & REFLECTIONS
   • 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 <-----