Unit 3 - Lesson 3 - Converting Standard to Intercept Form 3... · Pre-AP Algebra 2 Unit 3 – Lesson 3 – Converting Standard Form to Intercept Form Objectives: The students will

Pre-AP Algebra 2 Unit 3 – Lesson 3 – Converting Standard Form to Intercept Form Objectives: The students will be able to

• Convert from standard form to intercept form by factoring quadratic functions • Factor with any value as a in 𝑓 𝑥 = 𝑎𝑥! + 𝑏𝑥 + 𝑐

Materials: Do Now worksheet; pairwork; hw #3-3

Time Activity 5 min Review Homework

Show the answers to hw #3-2 on the overhead. Students correct their answers. Pass around the tally sheets.

10 min Homework Presentations Review the top 2 or 3 problems.

15 min Do Now Students will practice multiplying binomials to help review the patterns they will need in factoring

30 min Direct Instruction Background:

• Factoring: to break a number or expression down into a product of factors (a multiplication problem). For example: 12 = (3)(4), 2x + 6 = (2)(x + 3)

• Polynomial: a sum of monomial terms, such as 2x2 – 5x + 3 Concepts:

• When factoring a quadratic 1) If the GCF of the terms is greater than 1, factor it out. 2) If you have 2 terms, is it a Difference of Squares: a2 – b2. This is one of the most

important factoring patterns. Memorize it! § a2 – b2 = (a – b)(a + b).

3) If you have 3 terms, look at a, the coefficient of x2. § If a = 1 (i.e. no number in front of the x2), use the t-table method.

• Find the factors of c whose sum is b. • Try it in your head first. If you can’t find it, make a t-table.

§ If a > 1, use the box/ grouping method • find two numbers whose sum is b and product is ac. • Break the middle term into two parts based on those factors.

§ Some trinomials can’t be factored: they are called “prime”, just like numbers that can’t be factored.

§ Check result by multiplying factors. Examples:

1. Factor: 6x5 + 9x3 (show how to write out prime factorizations as an aid) 2. Factor x2 − 25

3. Factor 64−9x2

4. Factor: x2 − 4x −12 5. Factor: x2 + 2x − 4 (prime) 6. Factor: 3x2 − 27x + 60 (factoring out the GCF makes this much easier to do) 7. Factor 6x2 −19x +15

8. Find the x-intercepts of f (x) =14x2 +5x −1

20 min Pairwork Show students how to generate factorable trinomials by starting with a pair of binomials and multiplying them. You can make it more difficult by distributing a number across the entire trinomial. Ask students to generate 3 factorable trinomials, 1 of which has a GCF greater than 1, and one prime trinomial. Write the problems on a sheet of binder paper and switch with their partner. Partners should then try to factor the trinomials that they receive.

Pre-AP Algebra 2 Name: _______________________ Lesson #3-3: Do Now

Multiplying Binomials Part 1: Find the greatest common factor and describe the process you used:

(1) 24, 36, 60

(2) 8x2y3, 12x3y, 20x2y2

(3)

Part 2: Expand the following

(1) (x + 4)(x + 3)

(2) (x – 4)(x – 3) (3) (x + 4)(x – 3) (4) (x – 4)(x + 3) (5) Discuss what makes the middle and last terms + or −.

Part 3: Expand the following

(1) 𝑥 − 3 !

(2) 2𝑥 + 3 !

(3) 𝑥 − 4 ! (4) (𝑥 + 3)(𝑥 − 3)

(5) 2(𝑥 + 3)(𝑥 − 3)

(6) 2𝑥 + 3 2𝑥 − 3

(7) (2𝑥 + 1)(3𝑥 − 5) (8) (2𝑥 − 1)(3𝑥 + 5)

Pre-AP Algebra 2 Name: _______________________ Lesson #3-3: Pairwork

Basic Factoring Practice 1) Convert to intercept form. Then, match each function to its graph. 𝑓 𝑥 = 𝑥! − 4 𝑓 𝑥 = 𝑥! + 5𝑥 + 4 𝑓 𝑥 = 2𝑥! − 𝑥 − 15 𝑓 𝑥 = 15𝑥! − 31𝑥 − 12 A B

C D

Pre-AP Algebra 2 Name: _______________________ Lesson #3-3: Pairwork 2) Convert to intercept form. Then, find the x-intercepts and vertex.

a. f (x) = x2 −15x + 56. b. 𝑓 𝑥 = 3𝑥! + 2𝑥 − 16

3) Here is a window into the mind of Ms. Nicewarner… oooohh.. scary… This is how I come up with trinomial problems for you to factor: I start with the answer I want (the two binomial factors), I multiply them together, and that’s it! To make it more challenging, I may multiply all the terms in the trinomial by some number or expression – that will create a trinomial with a GCF that can be factored out. Now you try it. Create a mini-worksheet with three factorable trinomials. Make one of them have a GCF greater than 1. Then, trade papers with a partner and factor each other’s trinomials. Do the work on a different piece of paper and just write the trinomials in the spaces below.

Pre-AP Algebra 2 Name: ________________________ Lesson #3-3: Pair Work

My First Factoring Worksheet Factor each of the following trinomials completely. 1) 2) 3)

Pre-AP Algebra 2 Name: _______________________ Lesson #3-3: Homework

HW #3-3: Quadratics in Intercept Form Check for Understanding Can you complete these problems correctly by yourself 1) Find the x-intercepts for each function by factoring. Then, match each function to its graph.

Remember, always check first to see if the GCF is greater than 1.

a. f (x) = x2 + 2x − 48 b. f (x) =10x2 −50x +60 c. f (x) = 4x2 − 4x −15 d. f (x) = 6x2 −34x −12

I II

III IV

Pre-AP Algebra 2 Name: _______________________ Lesson #3-3: Homework 2) For each problem, write a quadratic equation that has the given x-intercepts. Expand out your

equation (i.e. don’t leave it written in factored form). Also, make sure that all of the coefficients are integers.

a. x = 5 and x = -5 b. x = ±½ c. x = 7 and x = -3 d. x = -¼ and x = ¾

Spiral What do you remember from Algebra 1and our previous units? (these are skills we will need in this unit) Work on a separate sheet a paper

1. Find the vertex and x-intercepts of 𝑓(𝑥) = − 𝑥 + 8 ! + 1. Then graph 𝑓(𝑥). Use your graph to answer the remaining questions.

2. 𝑓 −7 =

3. 𝑓 −9 =

4. 𝑓 −5 =

5. What value(s) of x make the following true

a. 𝑓 𝑥 = 0

b. 𝑓 𝑥 > 0

c. 𝑓 𝑥 ≤ 0

d. 𝑓 𝑥 = −3  

e. 𝑓 𝑥 ≥ −3

f. 𝑓 𝑥 < −3