Name Date ______________ HSA.REI.B.4.B Class

Determine the best method of solving a quadratic equationKey Takeaways:

Standard: Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.

There are several different methods that can be used to solve a quadratic equation, such as factoring, completing the square, and using the QF. To solve a given quadratic equation, it’s important to identify what information is given by analyzing a, b, and c, so that you can choose the best method for solving.

There are several different methods that can be used to solve a quadratic equation, such as factoring, completing the square, and using the QF. To solve a given quadratic equation, it’s important to identify what information is given by analyzing a, b, and c, so that you can choose the best method for solving.

Vocabulary: Factoring, quadratic formula, completing the square roots, solutions, zeroes

______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________Part 1: Activation of Prior Knowledge

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Based on the student work below, which of the following can we conclude? Select all that apply.

(1)This quadratic can be factored.(2)This quadratic equation can be solved using the quadratic formula.(3)This quadratic equation can be solved by completing the square.(4)This quadratic cannot be factored.

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Part 2: Guided Practice

Example 1: Justin was asked to solve the quadratic equation below:

−10=x2+4 x−12He did the following:

0=x2+4 x−20=¿

Part A: What method was Justin trying to use? Would it work? Why or why not?

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Part B: Solve the equation in the space below:

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Example 2: Seavy was trying to solve the quadratic equation f ( x )=3 x2+11 x−20 to find the roots and determined the roots were x=−4

3 and x=5.

Part A: Are the two roots correct? Justify your answer in the space below.

Part B: Factor f (x) to find the roots algebraically.

Method Pros ConsCalculator Very easy

Can be used to estimate Hard when the values

are not integers Not always an option

(may not have access to a calculator)

Factoring Step-by-step process Once practiced, can be

easy

Not all quadratics are factorable.

Will not work when solutions are irrational

Completing the square

Can be used to solve any quadratic

Can be used to solve quadratic where A is 1 and B is even fairly easily

Complex process Hard when B is not

even, and when A is not equal to 1

Quadratic Formula Can be used for ANY quadratic equation

Clear step-by-step process Easier than completing the

square when A is not 1.

Complex process Time consuming Easy to make small

mistakes

Part 3: Independent Practice (MILD)4

1. What are the roots of the quadratic below?

g ( x )=x2−10 x−24

(1) x=12∧x=−2(2) x=−12∧x=2(3) x=−6∧x=−4(4) x=6∧x=4

2. Which of the following quadratic equations can be solved using factoring?

(1)0=x2+5 x−4(2)0=x2−3 x−2(3)0=x2+5 x+4(4)0=x2+4 x+5

On the lines below, explain why you selected the answer you selected:

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

3. What are the solution(s) to the equation below?5=x2+4 x−8

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(1) x=2±√17(2) x=−2±√17(3) x=4±√17(4) x=−4±√17

On the lines below, explain why you selected the answer you selected:

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

4. Find the zeroes of the function below algebraicallyg ( x )=( x+5 )2−30

(1) −10±√30(2) −5±√30(3) 5±√30(4) No solution

On the lines below, explain why you selected the answer you selected:

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

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Part 4: Independent Practice (MEDIUM)

1. Given g ( x )=3 x2−4 x+10 and k ( x )=2 x2+16 x+8, solve the equation g ( x )=12k ( x )

algebraically for x.

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2. Tevon was solving the equation below:

0=4 x2−49

He took the following steps:0=A2−49

0=(A+7 ) ( A−7 )Part A: Solve the equation to find the value(s) of x that make the equation true.

Part B: What method was Tevon trying to use? What does A stand for?

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

3. Consider the quadratic below.

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Part A: Use the method of your choice to solve for the zeroes of the quadratic below. Please express the value(s) of x rounded to the nearest hundredth.

g ( x )=3 x2+5 x−10

Part B: What method did you choose to use to solve for the zeroes? Why?

____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

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Part 5: Independent Practice (SPICY)

1. Below is a table that shows the amount of money Tiara would have in a bank account based on the number of CDs bought, x. The amount she would have in her account depends on which store she buys CDs from.

4 CDs 6 CDS 8 CDS 10 CDsBest Buy $120 $95 $70 $45Amazon $138 $122 $106 $90

Part A: How much money did Tiara start with? How can you tell? Remember to include units.

__________________________________________________________________________________________________________________________________________________________________________________________________________________

Part B: For each store, is the relationship between # of CDs bought and money in her account linear or non-linear? How can you tell?

__________________________________________________________________________________________________________________________________________________________________________________________________________________

Part C: Does it make sense that this would be the type of relationship based on your real world experience? Why or why not?

__________________________________________________________________________________________________________________________________________________________________________________________________________________

Mathletes

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“”I’m a mathlete

1. Brandon needs to make over $120 next week. He makes $9 an hour babysitting and $12 an hour working at Sweet Green. He wants to work less than 12 hours.

Part A: Write a system of inequalities that represents this situation using x to represent the number of hours spent babysitting and y to represent the number of hours at Sweet Green.

Part B: Please graph the system of inequalities on the coordinate plane and identify one possible combination that would satisfy both inequalities.

Name Date ______________ HSA.REI.B.4.B Class

Determine the best method of solving a quadratic equationExit Ticket

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Directions: Complete each problem by showing ALL work. Don’t forget to use MOLE!

1. Given g ( x )=2 x2+3 x+10 and k ( x )=2 x+16, solve the equation g ( x )=2k ( x ) algebraically for x, to the nearest tenth.

2. Explain why you chose the method that you used to solve the equation in #1.________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

3. What are the solution(s) to the equation below?4=x2−6x−12

Name Date ______________ HSA.REI.B.4.B Class

Determine the best method of solving a quadratic equationHomework

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Directions: Solve each problem. Show all work using MOLE.

1A. What is the solution set of the equation below?2 x2+4 x−3=x2+x+15

1B: What method did you use to solve the quadratic equation above? Why?______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

2. What are the roots of the quadratic below?4 x2−3x+1=0

3. A tree was 9 feet tall when it was planted. After three months it was 11 feet tall. How fast is the tree growing?

4. How many solutions are there to the system of equations below?

−4 x+2 y=102 x− y=−5

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(1) 23 feet per month

(2) 32 feet per month

(3) 2 feet per month(4) 3 13 feet per month

(1) No solutions(2) 1 solution(3) 2 solutions(4) There is not enough information to

be able to tell

5. What is the axis of symmetry of the quadratic below?

y=−x2−5x+10

(1) x=−5(2) x=5

(3) x=52

(4) x=−52

6. A square has an area of 9 x2+6 x+1. What is the side length of the square?

(1) 3 x(2) 3 x+1(3) x+1(4) 9 x+1

7. What is the product of the factors below?(3 x2−4 x+1 ) (2 x−9 )

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