Characteristics of polynomial graphs

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  1. Investigating the Graphs of Polynomial Functions
    Recognize the characteristics of polynomial graphs from the following quadratic and cubic functions:
    P(x)=x23x10P\left( x \right) = {x^2} - 3x - 10
    P(x)=x2+3x+10P\left( x \right) = - {x^2} + 3x + 10
    P(x)=x33x210xP\left( x \right) = {x^3} - 3{x^2} - 10x
    P(x)=x3+3x2+10xP\left( x \right) = - {x^3} + 3{x^2} + 10x
    1. Graphing Polynomials
      Sketch the following polynomials:
      1. P(x)=(x3)(x1)(x+2)(x+5)P(x)=(x-3)(x-1)(x+2)(x+5)
      2. P(x)=(x5)(x2)(x+1)(x+4)(x+6)P(x)=-(x-5)(x-2)(x+1)(x+4)(x+6)
      3. P(x)=x22x+8P(x)=-x^2-2x+8
      4. P(x)=x38x2+15xP(x)=x^3-8x^2+15x
    2. Identifying Polynomial Graphs
      Which of the following could be the graph of a quadratic function with a negative leading coefficient?
      Characteristics of polynomial graphs
      Topic Notes
      characteristics of polynomial graphs