1. Quadratic Functions (3.1)

2. Identifying the vertex (e2, p243) Complete the square

3. Identify both the vertex and the x intercept (e3, p244) Factor it Given vertex and a point find the equation of a parabola (e4) (p244)  plug in all 4 values given.

4. Higher Degree Polynomials (3.2) negative coefficient reflects the graph in the x-axi Degree is odd upward shift, by one unit left shift, by one unit

5. the degree is odd and the leading coefficient is negative, the graph rises to the left and falls to the right the degree is even and the leading coefficient is positive, the graph rises to the left and right the degree is odd and the leading coefficient is positive, the graph falls to the left and rises to the right The Leading Coefficient Test only tells you whether the graph eventually rises or falls to the right or left. Other characteristics of the graph, such as intercepts and minimum and maximum points, must be determined by other tests.

6. Page 255

9. Apply Leading Coefficient Test. Because the leading coefficient is positive and the degree is even, you know that the graph eventually rises to the left and to the right

10. Example 11 (P274): Find the zeros of Step1: plot the graph – let the calculator/computer do the work There is a zero here, between 0.6 and.07 Step2: Rational Zero Test (P270) Setp3: Test Plug it into the calculator, don’t try to evaluate it by hand Yes 2/3 is a zero

11. x3x3 x2x2 xc 2/36-43-2 402 6030 Setp4: Synthetic Division Remainder is 0  Another proof that 2/3 is a zero 6(2/3) Remainder and factor theorems on page 268; e5,6 We will skip the upper and lower bound rule on page 258 6x 2 3 x-2/36x 3 -4x 2 3x-2 6x 3 -4x 2 3x-2 0 Now the long division is much easier (p264, e1,2,3)

12. Example 3 (p28): Possible zeros, repeated (touches)? A zero Step1: Plot it Step2: Rational Zero Test (p 256) x5x5 x4x4 x3x3 x2x2 xc -21012-128 -24-1016-8 1-25-840 x4x4 x3x3 x2x2 xc 11-25-84 14-4 14-40 x3x3 x2x2 xc 114-4 104 1040 Setp3: Test: Plug in 1 and 2 Setp4: Synthetic Division

13. Example 1, p286 As x (input) gets bigger y (output) gets smaller As x (input) gets smaller y (output) gets larger domain asymptote a straight line associated with a curve such that as a point moves along an infinite branch of the curve the distance from the point to the line approaches zero and the slope of the curve at the point approaches the slope of the line Rational Functions and Asymptotes (3.5)

14. Degree of the numerator is equal to the degree of the denominator Horizontal asymptote: y= ratio of leading coefficients Degree of the numerator is less than the degree of the denominator Horizontal asymptote: y = 0 Vertical asymptotes: set the denominator equal to zero and solve the resulting equation for x

15. Degree of the numerator is greater than the degree of the denominator No horizontal asymptote

16. Example 4 (p289)

17. Example 5 (p290)

18. Degree of numerator < denominator  Horizontal asymptote y = 0 Example 3 (p298)

19. x2x2 xc 1 0 2 1-22 Synthetic Division Slant Asymptotes – Page 299 Slant asmyptote

20. x2x2 xc 11-2 10 10 Example 5 (p299) Slant asmyptote