Name Date ______________ HSA.REI.B.4.B Class Determine the best method of solving a quadratic equation Key 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 ___________________________________________________________________________ _________________________________________________________________ ___________________________________________________________________________ _________________________________________________________________ ___________________________________________________________________________ _________________________________________________________________ ___________________________________________________________________________ _________________________________________________________________ ___________________________________________________________________________ _________________________________________________________________ 1
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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 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?
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.
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 )