Characteristics of polynomial graphs

Lessons

1. Investigating the Graphs of Polynomial Functions
   Recognize the characteristics of polynomial graphs from the following quadratic and cubic functions:
   i)
   $P\left( x \right) = {x^2} - 3x - 10$
   ii)
   $P\left( x \right) = - {x^2} + 3x + 10$
   iii)
   $P\left( x \right) = {x^3} - 3{x^2} - 10x$
   iv)
   $P\left( x \right) = - {x^3} + 3{x^2} + 10x$
2. Graphing Polynomials
   Sketch the following polynomials:
   1. $P(x)=(x-3)(x-1)(x+2)(x+5)$
   2. $P(x)=-(x-5)(x-2)(x+1)(x+4)(x+6)$
   3. $P(x)=-x^2-2x+8$
   4. $P(x)=x^3-8x^2+15x$
3. Identifying Polynomial Graphs
   Which of the following could be the graph of a quadratic function with a negative leading coefficient?