1 / 12

Warm-Up

DEGREE is Even/Odd, LEADING COEFFICIENT is Positive/Negative, END BEHAVIOR EXTREMA (Max or Min, Relative or Absolute). Warm-Up. (-2, 15). EVEN (2) POS (3) END BEHAVIOR x  ±∞; f(x)  ∞ (4) A. Min: (7, -21) R. Min: (-9, -8) R. Max: (-2, 15). ODD (2) NEG

dbutts
Download Presentation

Warm-Up

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. DEGREE is Even/Odd, • LEADING COEFFICIENT is Positive/Negative, • END BEHAVIOR • EXTREMA (Max or Min, Relative or Absolute) Warm-Up (-2, 15) • EVEN • (2) POS • (3) END BEHAVIOR x  ±∞; f(x)  ∞ • (4) A. Min: (7, -21) • R. Min: (-9, -8) R. Max: (-2, 15) • ODD • (2) NEG • (3) END BEHAVIOR x  - ∞; f(x)  ∞ • x  ∞; f(x) - ∞ • (4) R. Min: (-3, 4) R. Max: (8, 9) [1] [2] (8, 9) (-3, 4) (-9, -8) (7, -21) [3] [4] • EVEN • NEGATIVE • END BEHAVIOR • Absolute Max:Relative Max:Relative Min: • ODD • POSITIVE • END BEHAVIOR • Relative Max:Relative Min:

  2. Factoring Polynomials Review: [1]Difference of SQUARES Example [2]Difference of CUBES Example [3]Sum of CUBES Example

  3. [4]Factoring Trinomials: ax2 + bx + c Example Multiply = -12| Add = -4 -6 * 2 = 12; -6 + 2 = -4 Step #1:Find the factor pair (n1and n2) that MULTIPLY = ac(outsides) and ADD = b(middle). Step #2:Split the middle termbx = n1x + n2x Step #3:Perform factor by grouping on ax2 + n1x + n2x + c GCF of ax2 + n1x and GCF n2x + c = (?x + ?) (?x + ?)

  4. Factoring Polynomials: PRACTICE a) b) c) e) d) f)

  5. U – SUBSTITUTION: Step #1:Must have a trinomial in which one power of x is DOUBLE the other. ax2n + bxn + c = 0 Step #2:Let u equalsmaller exponent of x u = xn Step #3:SUBSTITUTE u into the trinomial to create a quadratic equation. au2 + bu + c = 0 Step #4:Use FACTORING or QUADRATIC FORMULA to find roots for u and solve for xn. u = Root #1 and u = Root #2  xn = Root #1 and Root #2

  6. EXAMPLE of U – SUBSTITUTION: • x4 – 16x2 + 60 = 0 • Step #1: x4 is double the x2 exponent • Step #2: u = x2 • Step #3: u2 – 16u +60 = 0 • Step #4: Solve u2 – 16u +60 = 0 • Factoring: (u – 10)(u – 6)=0 • Roots: u = 10 and u = 6  x2=10 and x2=6 • Solve for x:

  7. e) f) Example 1: Quadratic Form Only If possible, identify the variable term for u and write each equation in quadratic form using U-SUBSTITUTION. a) 2x6 + x3 + 9 = 0 b) x4 + 2x2 + 10 = 0 Let u = x3, 2u2 + u + 9 = 0 Let u = x2, u2 + 2u + 10 = 0 d)x7 + 2x2 + 10 = 0 c)7x10 – 6 = 0 Not Possible: No second x term to use Not Possible: x7 is more than double x2 power Let , u2 - 2u + 8 = 0 Let , u2 - 5u + 10 = 0

  8. b) Example 2: Solve using U-SUBSTITUTION Check to factor substituted quadratic form. a)

  9. Example 2: U-Substitution Part 2 Check to factor substituted quadratic form. c) d)

  10. f) Example 2: U-Substitution Part 3 Check to factor substituted quadratic form. e) Cannot square -4 …because there is no number that multiples by itself to equal -4

  11. Example 2: U-Substitution Part 4 Check to factor substituted quadratic form. g) h) i) j)

  12. Example 3: Solving Equations of Perfect Cubes Factor and Apply Quadratic Formula b) a) c) d)

More Related