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Quadratic Equations

Learn how to solve quadratic equations using Zero Product Property, Square Root Property, Completing the Square, and Quadratic Formula. Understand Discriminant and variable isolation. Examples provided for each method.

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Quadratic Equations

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  1. Quadratic Equations

  2. 1. Solve Quadratic Equations by Using the Zero Product Property 2. Solve Quadratic Equations by Using the Square Root Property 3. Complete the Square 4. Solve Quadratic Equations by Using the Quadratic Formula 5. Use the Discriminant 6. Solve an Equation for a Specified Variable

  3. Solve Quadratic Equations by Using the Zero Product Property If mn = 0, then m = 0 or n = 0

  4. Example 1: Solve

  5. Example 2: Solve

  6. 1. Solve Quadratic Equations by Using the Zero Product Property 2. Solve Quadratic Equations by Using the Square Root Property 3. Complete the Square 4. Solve Quadratic Equations by Using the Quadratic Formula 5. Use the Discriminant 6. Solve an Equation for a Specified Variable

  7. Solve Quadratic Equations by Using the Square Root Property

  8. Example 3: Solve

  9. Example 4: Solve

  10. Example 5: Solve

  11. 1. Solve Quadratic Equations by Using the Zero Product Property 2. Solve Quadratic Equations by Using the Square Root Property 3. Complete the Square 4. Solve Quadratic Equations by Using the Quadratic Formula 5. Use the Discriminant 6. Solve an Equation for a Specified Variable

  12. Complete the Square Step 1 Divide both sides by a to make the leading coefficient 1. Step 2 Isolate the variable terms on one side of the equation. Step 3 Complete the square. Add the square of one-half the linear term coefficient to both sides. Factor. Step 4 Apply the square root property and solve for x.

  13. Example 6: Solve Step 1 Step 4 Step 2 Step 3

  14. Example 7: Solve

  15. Example 8: Solve

  16. 1. Solve Quadratic Equations by Using the Zero Product Property 2. Solve Quadratic Equations by Using the Square Root Property 3. Complete the Square 4. Solve Quadratic Equations by Using the Quadratic Formula 5. Use the Discriminant 6. Solve an Equation for a Specified Variable

  17. Solve Quadratic Equations by Using the Quadratic Formula

  18. Example 9: Solve

  19. Example 9 continued: Solve (compare to completing the square)

  20. 1. Solve Quadratic Equations by Using the Zero Product Property 2. Solve Quadratic Equations by Using the Square Root Property 3. Complete the Square 4. Solve Quadratic Equations by Using the Quadratic Formula 5. Use the Discriminant 6. Solve an Equation for a Specified Variable

  21. Use the Discriminant is called the discriminant.

  22. Use the Discriminant is zero  1 real solution

  23. Use the Discriminant is positive 2real solutions

  24. Use the Discriminant is negative 2 imaginary solutions

  25. 1. Solve Quadratic Equations by Using the Zero Product Property 2. Solve Quadratic Equations by Using the Square Root Property 3. Complete the Square 4. Solve Quadratic Equations by Using the Quadratic Formula 5. Use the Discriminant 6. Solve an Equation for a Specified Variable

  26. Example 10: Solve for a

  27. Example 11: Solve for x

  28. Example 12: Solve for y

  29. Example 12 continued:

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