Quadratic Functions

Quadratic Functions

1. Quadratic formula

   • Rootrs/Zeros
   • Discriminant
     • b^2-4ac
       • Example if: if b^2-4ac=o we have no roots
       • If b^2-4ac>o, we have two dinstinct roots
       • if b^2<, we have two imaginary roots
   • x=-b+-^.5 b^2-ac/2

2. Standard form

   • ax^2+bx+c=0
     • To solve
       • You can Factor it
         • example
           • x^2+-5x+4=0
             • (x-4)(x-1)
               • Example of finding the squares
       • Or use quadraic formula
   • c value is the y-intercept
   • Graphing
     • changes in c
       • if c>0, parabola moves up
       • if c<0, the parabola moves down
     • changes in b
       • b>0, vertex movs down and left
       • b<0, vertex moves dow and right
   • to get to vertex form you complet the square

3. Vertex form

   • a(x-h)^2+k
     • example
       • a(3-1)+8
         • if a is negitive, the parabla opens up
         • if a is positive the graph opens down
     • To slove
       • Isolate 'x'
     • H and K are = to vertex
       • If a>0, vertex is minimum
       • If a<, vertex is maximum
     • changes in K
       • if K>0, the parabola shifts up
       • if k<0 the parabola shifts down
   • changes in h
     • if h>o, the parabola shifts right
     • if h<o, the parabala shifts left

4. Factored form

   • a(x-s)(x-t)
     • example
       • a(x-7)(x+7)
   • To solve
     • set each factor to = 0

5. Graphing

   • Parabola
     • Positive
     • negitive
   • vertex
   • x/y intercept
   • x/y coordinats
   • Translations
     • horazontal
     • vertical
   • shift and step method