Lesson 6.notebook

Lesson 6.notebook
March 24, 2015
Warm Up
Unit 4 Review Homework
1. Determine if the function is EVEN or ODD
a. y = x2 ­ 3x + 4
b. y = x4 ­ x2
1. 6x4 + 3x3 ­ 10x2 ­ 3x
3. 11x4 + 8x3 + 6x2
5. 5x ­ 39x + 28
7. 24n3 ­ 34n2 ­ 36n + 32
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9. (x ­ 2)(x2 + 2x + 4)(x+2)(x2 ­ 2x + 4)
2. If a toy rocket is launched vercally from ground level with an inial velocity of 128 feet per second, then its height h aer t second is given by the equaon h(t) = ‐16t2 + 128t.
11. (x ­ 5)(x + 5)
13. (x ­ 3)(x + 3)(x2 ­ 6)
a. How long will it take for the rocket to return to the ground?
45. 4x5
b. How long will it take the rocket to hit its maximum height?
49. 2u4v
46. 64m6n6
47. x3
48. 2n8m
50. 3x3
y3
c. What is the maximum height? Mar 23­7:22 PM
Write Equations of Polynomials Given Zeros
15. (x + 5)(x2 ­ 5x + 25)
Mar 24­7:19 AM
1. Write each zero as a factor (x ­ #)
Find the polynomial of least degree that has the following zeros. Identify the degree of the resulting polynomial.
2. Multiply the factors
1. (3,0)(­2,0)
2. (0,0),(­2,0)
3. (3,0), (­2,0), (1,0)
4. (6,0),(4,0),(­2,0),(1,0)
EXAMPLE: 3, 5
Mar 23­7:26 PM
Applications of Polynomials
You have a rectangular box has sides whose lengths (in inches) are (x + 2), (x ‐ 2) and (2x + 1)
Mar 24­7:46 AM
A pool has dimensions of (x + 1), (4x + 7) and (2x ­ 5). a. What is the volume of the pool?
a. Write a polynomial model, in standard form, for the volume of the box. b. Use the model to find the volume when x is equal to 5 inches.
Mar 23­7:27 PM
b. What is the value of x if the volume of the pool is 10,000 cubic feet?
Mar 24­10:14 AM
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Lesson 6.notebook
March 24, 2015
. GIVEN A VOLUME, FIND THE DIMENSIONS
Write a polynomial to model the volume
•
Type this polynomial into y1 = •
Type in the amount (#) for the volume into y2 =
•
Find the intersection!
•
You are designing a rectangular box for LEGO storage. Your model is a
and
rectangular prism with side lengths (inches) ,
the capacity of the LEGO storage box to be 2000 cubic inches. What is the
approximate measurement for x? Round to the nearest hundredth.
An open box is to be made from a 10‐in. by 12‐in. piece of cardboard by cutting x‐
in. squares from each corner and folding up the sides. a. Write a function giving the volume of the box in terms of x. . You want
b. Sketch a graph of the function and use it to approximate the value of x that produces the greatest volume.
Mar 23­7:30 PM
Mar 23­7:31 PM
A box is made from a piece of cardboard that is 18 by 20 inches. What is the volume of the box if a notch (x) is cut out of each corner? What is the value of x to produce a maximum volume?
Mar 24­10:15 AM
Mar 24­8:42 AM
Mar 24­8:42 AM
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