What are characteristics of polynomial graphs?

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

Characteristics of polynomial graphs