1 / 13

Pre-Calculus

Pre-Calculus. Chapter 2 Review. Vocabulary. Standard (Vertex) Form of a parabola Vertex and Roots of a Parabola Equation from Point and Vertex End Behavior Graphing Polynomials Long Division, Synthetic Division, Remainder Theorem Complex Number Operations

fulbright
Télécharger la présentation

Pre-Calculus

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Pre-Calculus Chapter 2 Review

  2. Vocabulary • Standard (Vertex) Form of a parabola • Vertex and Roots of a Parabola • Equation from Point and Vertex • End Behavior • Graphing Polynomials • Long Division, Synthetic Division, Remainder Theorem • Complex Number Operations • Solutions to Quadratics, Discriminant • Rational Root Theorem • Type and Number of Roots, Descartes’ Law of Signs, Bounds • Finding all complex roots • Asymptotes: (Horizontal Vertical Slant Holes) • Graphing Rational Functions • Partial Fractions

  3. Answer: 4th degree polynomial Even degree polynomial 1.) Give the degree of the polynomial with the graph below:

  4. Answers: 2.) 4 zeros 3.) Real zeros 2.) Give the number of zeros of that polynomial3.) Give the types of zeros of that polynomial

  5. 4.) If 2i is a zero of a polynomial, what else must also be? Answer: -2i must also be a zero by the conjugate pair theorem

  6. 5.) If f(2) = 4, and f(4) = -2, what must occur between x = 2 and x = 4? Answer: There must be a zero between x=2 and x=4 by the IVT

  7. What are the possible numbers of positive and negative real zeros of the function? Answer: 4, 2, or 0 positive real roots 0 negative real roots What are its possible rational roots? Answer: 6.) Given the polynomial ,

  8. 7.) Decompose the fraction into its partial fractions. Answer: Let x = 1 Let x = 7

  9. Find an upper and lower bound for the zeros of the function Upper: x = 2 Lower: x = -6 Use synthetic division to show that 2 is a root of the function. Use the remainder theorem to show that –2 is also a root of the function. Use the quadratic formula and factoring to find the remaining zeros. 8.) Given:

  10. Find the discriminant of the equation D = -16 Tell what the discriminant says about the equation. Non-real Zeros Complete the square to find the zeros of the equation. 9.) Given:

  11. VA: x = 3, x = -1 HA: y = 0 VA: x = -2 Hole: (2, .25) HA: y = 0 10.) Give the asymptotes for each of the following.

  12. 10.) Give the asymptotes for each of the following. VA: x = 0 HA: None SA: y = x - 2.5

  13. Vertical Asymptote at x = 2 and x = -4, Horizontal Asymptote at y = 0, Hole at (3, x) No Vertical Asymptote, A Slant Asymptote, Hole at (-2, x) 11.) Give an equation for the rational function with the given properties.

More Related