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4.2 Solving Quadratic Equations without factoring (Due 1/18/24)

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37 questions
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Essential Question: What are other methods of solving quadratic functions besides factoring?


Learning Target: Students will be able to solve quadratic equations that model real-world situations.


Show your work for credit.

Day 1 1/16/24

Solving Equations by Taking Square Roots

Question 1
1.

Simplify

Question 2
2.

Review: All square roots of real, positive numbers have two solutions.

Question 3
3.

Does this square root have a real answer? (Hint is there a number times itself that equals -81)


Question 4
4.

Explain why all square roots have two answers.

Question 5
5.

Review: Match each number on the left with its simplified form on the right.

  • 4
  • -4
  • 5
  • -5
  • 6
  • -6
  • 8
  • -8
Required
5
Question 6
6.

Vocabulary: In your own words, what does it mean to isolate a variable?

Required
5
Question 7
7.

Vocabulary: In your own words, what is an inverse operation?

Question 8
8.

Match the operation with its inverse.

Draggable itemarrow_right_altCorresponding Item
inverse of to the second power
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subtraction
inverse of multiplication
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addition
inverse of subtraction
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division
inverse of division
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multiplication
inverse of addition
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square root
Question 9
9.

Question 10
10.

What is the first step to solving this equation?

2x - 14 = 50

Question 11
11.

What is the second step to solving this equation?

2x - 14 = 50

Question 12
12.

Solve this equation.

Question 13
13.

Solve this equation.

Question 14
14.

Solve this equation.


Question 15
15.

Solve this equation.



Question 16
16.

Solve this equation.



Question 17
17.

Solve this equation.


Question 18
18.

Solve this equation.

Question 19
19.

Below is an example how to solve an quadratic equation by taking a square root. Fill the blanks to complete the problem.

Question 20
20.

Solve this quadratic equation by taking the square root.


Question 21
21.

Solve this quadratic equation by taking the square root.


Day 2 1/17/24

Irrational Solutions

Question 22
22.

Solve this quadratic equation by taking the square root.


Question 23
23.

Solve this quadratic equation by taking the square root.

Question 24
24.

Solve this quadratic equation by taking the square root.


Question 25
25.

Solve this quadratic equation by taking the square root.

Question 26
26.

Solve this quadratic equation by taking the square root.


Question 27
27.

Solve this quadratic equation by taking the square root.


Question 28
28.

Solve this quadratic equation by taking the square root.


Question 29
29.

Solve this quadratic equation by taking the square root.

Question 30
30.

Below is an example how to solve an quadratic equation by taking a square root. Fill the blanks to complete the problem. Use desmos to solve the radical at the end of the problem.

Question 31
31.

Solve this quadratic equation by taking the square root.





Question 32
32.

Solve this quadratic equation by taking the square root.

Question 33
33.

Solve this quadratic equation by taking the square root.




Question 34
34.

Solve this quadratic equation by taking the square root.



Question 35
35.

Question 36
36.

Question 37
37.