1 / 22

Chapter 2 Preview

Chapter 2 Preview. Essential Question: How do we do this stuff?. Chapter 2 Preview. Use the x-intercept method to find all real solutions of the equation x 3 – 8x 2 + 9x + 18 = 0 Graph the function using the graphing calculator Find the roots Roots at -1, 3, & 6. Chapter 2 Preview.

duyen
Download Presentation

Chapter 2 Preview

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. Chapter 2 Preview Essential Question: How do we do this stuff?

  2. Chapter 2 Preview • Use the x-intercept method to find all real solutions of the equationx3 – 8x2 + 9x + 18 = 0 • Graph the function using the graphing calculator • Find the roots • Roots at -1, 3, & 6

  3. Chapter 2 Preview • Determine the nature of the roots2x2 – 12x + 18 = 0 • Use the discriminant to determine the number of roots: • Discriminant = 0 means “1 real solution”

  4. Chapter 2 Preview • Solve by taking the square root of both sides: (4x-4)2 = 25

  5. Chapter 2 Preview • Solve by factoring: x2 + 2x – 3 = 0 • Looking for two numbers that multiply to get -3 and add to get 2 • Only ways to multiply to get -3 are • 1 • -3 (they add to -2) • -1 • 3 (they add to 2) Hey! We got a winner! • Factor using those numbers • (x – 1)(x + 3) = 0 • Set each part of the factorization to 0 to get the solutions • x – 1 = 0 or x + 3 = 0 • x = 1 or x = -3

  6. Chapter 2 Preview • Solve by using the quadratic formulax2 – 2x – 5 = 0

  7. Chapter 2 Preview • Find all solutions: 5x = 2x2 - 1

  8. Chapter 2 Preview • Find all solutions: |4 – 0.2x| + 1 = 19

  9. Chapter 2 Preview • Find all solutions: |x2 - 10x + 17| = 8

  10. Chapter 2 Preview • Find all solutions:

  11. Chapter 2 Preview • Find all solutions:

  12. Chapter 2 Preview • The problem on the preview has no solution (square roots can’t ever be negative)Find all solutions:

  13. Chapter 2 Preview • Find all solutions: • Real solutions? When numerator = 0 • x2 + 1x – 42 = 0 • (x + 7)(x – 6) = 0 • x = -7 or x = 6 • Extraneous solutions? When denominator = 0 • x – 6 = 0 • x = 6 • When a solution comes up as real and extraneous, the extraneous solution takes precedence • Real solution: x = -7 • Extraneous solution: x = 6

  14. Chapter 2 Preview • Find all solutions: • Real solutions? When numerator = 0 • 5x2 + 44x + 63 = 0 • (5x + 9)(x + 7) = 0 • x = -9/5 or x = -7 • Extraneous solutions? When denominator = 0 • x2 + 12x + 35 = 0 • (x + 7)(x + 5) = 0 • x = -7 or x = -5 • When a solution comes up as real and extraneous, the extraneous solution takes precedence • Real solution: x = -9/5 • Extraneous solution: x = -7 or x = -5

  15. Chapter 2 Preview • Write -4 < x < 9 in interval notation • If an inequality has a line underneath it, we use braces; parenthesis without. • (-4, 9]

  16. Chapter 2 Preview • Solve the inequality and express your answer in interval notation: 2x – 6 < 3x + 8 • [-14, ∞)

  17. Chapter 2 Preview • Solve the inequality and express your answer in interval notation: -15<-3x+3<-3 • [2, 6]

  18. Chapter 2 Preview • Solve the inequality and express your answer in interval notation: • Critical Points • Real solutions: 5 & -9 • Extraneous solution: 1 • Test the intervals • (-∞, -9] use x = -10, get -15/11 > 0 FAIL • [-9, 1) use x = 0, get 45 > 0 PASS • (1, 5] use x = 2, get -33 > 0 FAIL • [5, ∞) use x = 6, get 3> 0PASS • Interval solutions are [-9, 1) and [5, ∞)

  19. Chapter 2 Preview • The simple interest I on an investment of P dollars at an interest rate r for t years is given by I = Prt. Find the time it would take to earn $1800 in interest on an investment of $17,000 at a rate of 6.9%. • You’re given I ($1800), P ($17,000) and r (6.9% = 0.069). • Just plug them into the equation and solve for t • 1800 / 17000 = (17000)(0.069)(t) / 17000 • 0.10588 / 0.069 = (0.069)(t) / 0.069 • 1.53 = t

  20. Chapter 2 Preview • d = -16t2 + 37. Find how long it takes the object to reach the ground (d = 0) • Because time is never negative, t = 1.5 s

  21. Chapter 2 Preview • 128t – 16t2. During what period of time is the arrow above 240 feet

  22. Chapter 2 Preview • #20, continued • 16t2-128t+240 < 0 • Test the intervals • (-∞, 3] -> test x = 0, get 240 < 0 FAIL • [3, 5] -> test x = 4, get -16 < 0 PASS • [5, ∞) -> test x = 6, get 48 < 0 FAIL • The arrow is above 240 ft. from 3 to 5 sec.

More Related