1. Relating Polynomial Functions and Equations Sketch the graph of a polynomial function whose equation is given in factored form. Determine an equation to represent a given graph of a polynomial function.

2. Quadratic Functions When the graph of a function intersects the x-axis, the x-intercepts are the zeros of the function and the roots of the corresponding equation. Roots are –2 and 1 Zeros are –2 and 1 Quadratic Function Quadratic Equation

3. Family of Functions Family of quadratics note -Zeros of order 2. The graph just touches here. Eg. y=a(x-2)(x-2) or y=(x-2) 2 There are many graphs with the same zeros. Depending on the value of ‘a’ they will be stretches, compressions or reflections of the basic curve. Family of cubics note – Zeros of order 2 or 3.Family of cubics For a zero of order 3 the graph crosses, but has a slope of zero. Eg. y=a(x+3) 3 (x+4); y=a(x+3) 3

4. Zeros and Roots of Polynomial Functions

6. Determine the Equation Go to Winplot to try to find the equation for each graph. Guess

7. Sketch the graph Sketch the graph of the functions. y=(x-3) 2 (x+4) 2

8. Sketch the graph Sketch the graph of the functions. y=(x+5)(x+1) 2