Mastering Quadratic Equations

Unit 3 Quiz 2 Review

A guide to understanding and solving quadratic equations by taking the square root and solving by factoring.

Solving Quadratic Equations

To solve quadratic equations by taking square roots, isolate the squared term on one side of the equation. Then, take the square root of both sides. Remember to consider both the positive and negative square roots. Example: r = ±6

Multiple Choice

What should you remember while taking square roots to solve quadratic equations?

• Only consider the positive square root

• Isolate the squared term on one side of the equation

• Take the square root of only one side of the equation

• Ignore the squared term while taking square roots

Quadratic Equation with no b term:

Trivia: To solve quadratic equations, it is important to isolate the squared term on one side of the equation. This allows you to take the square root of only one side, leading to the solution. Remember this key step while solving quadratic equations!

Solve each equation by taking square roots.
These are the questions from the review worksheet. Make sure that you have completed these problems on your worksheet before moving to the next slide.

1. Solve r² = 36.
2. Solve p² = 49.
3. Solve x² = 4.
4. Solve m² = 25.

Solve each equation by taking square roots.
Check your answers to the questions.

Solve each equation by taking square roots.
These are the questions from the review worksheet. Make sure that you have completed these problems on your worksheet before moving to the next slide.

5. Solve 36b² - 4 = 60
6. Solve 6n² + 8 = 494.
7. Solve 16x² - 6 = -2
8. Solve 9v² + 5 = 905

Solve each equation by taking square roots.
Check your answers to the questions.

Factoring Equations

Trivia: Factoring is a powerful technique used to solve equations. It involves breaking down an equation into its factors. In this case, the equation (a - 4)(a - 8) = 0 can be solved by setting each factor equal to zero. This allows us to find the values of 'a' that make the equation true. Factoring is commonly used in algebra to solve various types of equations.

Multiple Choice

Which of the following equations can be solved by factoring?

• 36b² - 4 = 60

• 16x² - 6 = -2

• p² = 49

• (a - 4)(a - 8) = 0

• m² = 25

Solve each equation by factoring.
These are the questions from the review worksheet. Make sure that you have completed these problems on your worksheet before moving to the next slide.

9. Solve (a - 4)(a - 8) = 0
10. Solve (p + 2)(p − 4) = 0
11. Solve (8a - 7)(7a + 3) = 0
12. Solve (x + 3)(x - 8) = 0

Solve each equation by taking square roots.
Check your answers to the questions.

Multiple Select

Which of the following equations is a quadratic equation?

• 9v² + 5 = 905

• (p + 2)(p − 4) = 0

• (8a - 7)(7a + 3) = 0

• v² - v - 20 = 0

Quadratic Equations

Trivia: Quadratic equations are equations of the form ax² + bx + c = 0, where a, b, and c are constants. They have the highest power of the variable as 2. The equation (8a-7)(7a+ 3) = 0 is a quadratic equation because it can be written in the form ax² + bx + c = 0.

Solving Quadratic Equations by Factoring

1. Write the equation in standard form: ax² + bx + c = 0
2. Use the x-method to find the roots.
3. Use the zero product property to find the solutions.
4. Write the solutions as a solution set. {a, b}

Multiple Choice

What is the first step in solving a quadratic equation?

• Isolate the quadratic term and simplify

• Make sure that the equation is in standard form

• Check the solutions by substituting them back into the original equation

• Understand the nature of the solutions

Solve each equation by factoring.
These are the questions from the review worksheet. Make sure that you have completed these problems on your worksheet before moving to the next slide.

13. Solve v² - v - 20 = 0
14. Solve n² - 16n + 64 = 0
15. Solve v² + v - 6 = 0
16. Solve n² - 64 = 0

Solve each equation by taking square roots.
Check your answers to the questions.

Solve each equation by factoring.
These are the questions from the review worksheet. Make sure that you have completed these problems on your worksheet before moving to the next slide.

17. Solve n² - 8n + 20 = 4
18. Solve n² + 4n - 23 = -2
19. Solve x² - 4x - 1 = -5
20. Solve n² - 5n + 5 = 5

Solve each equation by taking square roots.
Check your answers to the questions.

Open Ended

You must upload a picture of both sides of your worksheet to this slide in order to receive credit for completing the review.