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Mastering Quadratic Equations: Methods and Solutions

Learn how to solve quadratic equations using factoring, square roots, completing the square, and the quadratic formula. Understand the general form and different methods for solving to master this crucial aspect of algebra. Practice with examples and word problems.

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Mastering Quadratic Equations: Methods and Solutions

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  1. 1.4 Quadratic Equations

  2. General Form of a Quadratic Equation A quadratic equation is also known as a second-degree polynomial equation

  3. Methods for Solving • Factoring • Extracting the Square Roots • Completing the Square • Quadratic Formula

  4. Method #1 - Factoring Use the Zero-Factor Property If ab=0, then a=0 or b=0. **Remember** You can only use the Zero-Factor Property for an equation written in general form! First step has to be to set the equation equal to zero

  5. Solve By Factoring

  6. Extracting the Square Root

  7. Solve by Extracting the Square Root

  8. Method #2 – Completing the Square Extracting the Square Root is rather simple, but what if we had been given the last example in general form… Is it as easy? Well we can make it that easy by completing the square! 

  9. Completing the Square

  10. Solve by Completing the Square

  11. Complete the Square for the following… Notice anything???

  12. Method #4Quadratic Formula

  13. Number of Solutions can be determined by the DISCRIMINANT If D>0 (positive), then the quadratic equation has 2 distinct real solutions and 2 x intercepts. If D=0, then the quadratic equation has one repeated real solution and its graph has 1 x intercept. If D<0 (negative), then the quadratic equation has no real solutions and its graph has no x intercepts.

  14. Use the Quadratic Formula to Solve

  15. Try a Word Problem  A bedroom is 3 feet longer than it is wide and has an area of 154 square feet. Find the dimensions of the room.

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