10. Let’s try a few examples
61425
235
xxxy
45
24
xxy
xxxy 2
2
11. Middle behavior
• To get the middle behavior we need more
information:
– X Intercepts (zeros)
– Max/min points (extrema)
12. Zeros of polynomials
• Zeros are the same as x-intercepts.
• Zeros happen when f(x) = 0
Zero = solution = factor
If x = c is a zero of polynomial, then
x – c is a factor of the polynomial.
15. Practice
• Describe the end behavior
• Find the zeros of the function (manually)
• Graph the function on the graphing calculator
and find the relative extrema.
24
22)( xxxf
16. The Fundamental Theorem of Algebra
• Every polynomial of degree, n, has
exactly n roots.
• Repeated roots:
– An even number of repeats will touch the x-axis.
– An odd number of repeats will cross the x-axis.
17. To sketch the graph of a polynomial
function
1. Apply the leading coefficient test.
2. Find the zeros and y - intercepts
3. Plot a few points:
1. A few to the left of the zeros
2. A few to the right of the zeros
4. Complete the graph.