U7D13 Have out: Bellwork: pencil, red pen, highlighter, GP notebook 1. Write a standard (expanded) form equation of a quartic polynomial with the zeros 6i and . 2. Find the polynomial P(x) whose graph is given. (0, 6) y total:

1. Write a standard (expanded) form equation of a quartic polynomial with the zeros 6i and . Bellwork: +1 +1 +½ +½ +½ +½ +1 +1 P(x) = (x2 – 5)(x2 + 36) +1 P(x) = x4 + 36x2 – 5x2 – 180 P(x) = x4 + 31x2 – 180 +1 +1 +1 +1

Bellwork: 2. Find the polynomial P(x) whose graph is given. total: +½ +1 +1 (0, –6) y +1 +1 total: +1 +1 +2

Possible rational zeros 1. For each polynomial, use the Rational Root Theorem to: (i) list all possible rational zeros, (ii) find all zeros, (iii) sketch a graph of y = P(x). q p a) P(x) = 2x3 – 9x2 + 27 Possible rational zeros factors of 27 ±1, ±3, ±9, ±27 make combinations… factors of 2 ±1, ±2 3 try x = ____ 2 –9 27 –18 –3 +6 –9 –27 –6 3 3 2 –3 –9  x – 3 P(x) = 2x 2x2 –6x P(x) = + 3 + 3x –9

P(x) = 2x3 – 9x2 + 27 y P(x) = (x – 3)(2x2 – 3x – 9) (0, 27) 0 = (x – 3)(x – 3)(2x + 3) x – 3 = 0 2x + 3 = 0 x = 3 2x = –3 double zero x = –1.5 x (–1.5, 0) (3, 0) –1.5, 3, 3 x = _________

After the quiz, work on the rest of the worksheet. Quiz Time Clear your desk except for a pencil, highlighter, and a NON-GRAPHING calculator! After the quiz, work on the rest of the worksheet.