mr. sturdivant's class - home · web viewtoday, we learned how to identify and factor two...
TRANSCRIPT
Name Date _________ HSA.SSE.A.2 Class
Factoring Special Case QuadraticsKey Takeaways:
Standard: Use the structure of an expression to identify ways to rewrite it. For example, see x4 - y4 as (x2)2 - (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 - y2)(x2 + y2).
Previously, we learned how to factor trinomials of the form x2+bx+c. Today, we learned how to identify and factor two special case quadratics: difference of two perfect squares and perfect square trinomials
Vocabulary: Sum, difference, product, Perfect square trinomials, difference of two squares, Perfect squares, square roots, Quadratic, Binomial, trinomial, Combining like terms, Factors, factorable, Factor ‘completely’ ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________
Everybody Writes!________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________
Part 1: Activation of Prior Knowledge
1
1. Find a, b, and c for the quadratic x2−9, and then factor it. Use an area model to help you.
a=¿
b=¿
c=¿
Factors:
2
Part 2: Explore Part 1
1. What are the factors of x2−16?
2. What are the factors of 4 x2−16?
3. What makes these quadratics different than the quadratics we factored yesterday? What do the quadratics in #1 and #2 have in common?
__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________
4. Which of the quadratics below would follow the same pattern? Why?
(a)36 x2−16
(b)9 x2−25
(c)4 x2+16
______________________________________________________________________________________________________________________________________________________________________________________________________
3
Part 3: Explore Part 2
1. What is ( x+7 )2?
2. What is ( x−7 )2 as a simplified trinomial?
3. What is the relationship between each trinomial’s b and c term?
________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________
4. Which of the following quadratics would follow the same pattern? Why?(a)
x2+10x+24(b)
x2−10 x+25(c)
x2+5x+25
4
Part 4: Independent Practice (MILD)
1. Which of the following quadratics can be factored using the difference of squares?(1) 2 x2−100(2) x2−81(3) x2+81(4) 4 x2+9
2. Which of the following is a perfect square trinomial?(1) x2+6 x+36(2) x2+8 x+64(3) x2−10 x−25(4) x2−8 x+16
3. What is x2−121 in factored form?(a) ( x−11 )2
(b) ( x−11 ) ( x+11)(c) ( x−121 ) ( x+1 )(d) ( x+11)2
4. What is 9 x4−16x2 in factored form?(a) (3 x−4 ) (3x+4 )(b) (3 x2−4 ) (3 x2+4 )(c) (3 x2−4 ) (3 x2+4 x )(d) (3 x2−4 x ) (3 x2+4 x )
5. What is x2−8 x+16in factored form?(a) ( x+4 )2
(b) ( x−4 ) ( x+4 )(c) ( x−4 )2
(d) ( x−8 ) ( x−2 )
6. What is ( x+7 )2?(a) x2+49(b) x2−14 x+49(c)x2+49 x+49(d) x2+14 x+49
5
7. Factor the following polynomials:
A) k2 – 100
B) 36x2 – 49y2
C) 81 – r2
6
Part 5: Independent Practice (MEDIUM)
1. Which shows the correct factored form?
2. Factor 16 x4−81.
3. What is a common factor of x2−16and x2+ x−12? a. x – 4 b. x – 3c. x+3d. x+4
4. One of the factors of 16 x2– 9 is…a. 8 x – 3b. 8 x+3c. x+3d. 4 x –3
5. Expressed in factored form, the binomial 16a2 –81b2 is equivalent to…a. (4a – 9b)(4 a– 9b)b. (4a – 9b)(a+9b) c. (4a – 9b)(4 a+9b) d. (4a – 9b)(4 a+b)
Part 6: Independent Practice (SPICY)7
1. Justice uses the equation y=12 x+7 to calculate the cost of his babysitting. Aurel charges at a constant rate, and charges $18 for one hour and $57 for four hours. Which of the following statements is true?
(a) Justice’s hourly rate is $1 more expensive(b) Aurel’s hourly rate is $6 more expensive(c) Aurel’s initial fee is $2 cheaper(d) The two charge the same hourly rate
2. The table below shows the total amount a company charges a homeowner to clean the carpets in different numbers of rooms.
Which of the following equations represents the data in the table?(a) D= 129r+10
(b) D=3 r+7(c) D=29r(d) D=29r+10
3. Which of the following lines contains the point (-1, 4)?
(a) y=4 x(b) y=4 x+8(c) y=3 x−1(d) y=x−5
4. Which of the following shows the equation of the line that is parallel to the line that passes through the points (4, 3) and (-2, 1)?
8
(a) y=13 x+123
(b) y=13 x+5(c) y=3 x−9(d) y=3 x+7
Spicy: Open Ended Response
1. AT&T charges a flat monthly fee of $50 plus $0.75 per gb of storage uses. Verizon charges a rate of $35 plus $0.90 per gb used. After how many gb of storage would the two companies price be equal?
Answer: ________________GB
2. If you were planning on using 80 GB a month, which would you use? Why? Explain in the space below.
________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________
Mathletes1.
9
“”I’m a mathlete
2. The height of a ball tossed in the air is represented by the equation y=−x2+12 x+3, where y is the height in meters and x is the time in seconds. What is the maximum height reached by the ball? (Solve this problem algebraically, which means without using a graph! )
Genius Round: Find the solution to this system of equations
{f ( x )=x2+2xf ( x )=4 x−2
Name Date _________ HSA.SSE.A.2 Class
Factoring Special Case QuadraticsExit Ticket
10
Directions: Complete each problem by showing ALL work. Don’t forget to use MOLE!
1. What are the factors of the quadratic below?
x2−12 x+36
(1) ( x−6 ) ( x+6 )(2) ( x+6 )2
(3) ( x−6 )2
(4) ( x+9 ) ( x−4 )
2. What are the factors of the quadratic below?
16 x4−64
3. The factored form of a quadratic is (2 x−3 )2. Express the factored quadratic as a simplified trinomial.
11
Name Date _________ HSA.SSE.A.2 Class
Factoring Special Case QuadraticsHomework
Directions: Solve each problem. Show all work using MOLE.
1. What are the factors of 9 x2−25?
12
(a) (3 x – 5)(3x−5)(b) (3 x+5)(3x+5)(c) (9 x – 5)(x+5)(d) (3 x+5)(3x –5)
2. What is a common factor of x2+7x−18 and x2−81?
(a) (x – 9)(b) (x + 9)(c) (x + 2)(d) (x – 2)
3. Factor the expression below.
9 x4−36
Answer:_____________________________
4. Which of the following is equivalent to the expression below:
(4+5 x )2
(a)25 x2+16(b)−25 x2+16
5. What is the solution set to the system of equations seen on the graph?
(a)(-5, -4)(b)(-4, -5)(c) (4, -5)(d)(-4, 5)
13
(c) 25 x2+40 x+16
(d)25 x2−40 x+166. What are the factors of the quadratic
x2−8 x+15?
(a) (x+3)(x+5)(b) (x+3)(x−5)(c) (x−3)(x+5)(d) (x−3)(x−5)
7. According to the graph below, f (x)=2. What is the value of x?
(a) -2(b) -1(c) 0(d) 2
8. What is the y-intercept of the graph below? Describe its meaning.
14