1 / 17

Chapter 11

Chapter 11. Quadratic Functions and Equations. The Quadratic Formula. 11.2. Solving Using the Quadratic Formula Approximating Solutions. Solving Using the Quadratic Formula.

lesley-dyer
Download Presentation

Chapter 11

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 11 Quadratic Functions and Equations

  2. The Quadratic Formula 11.2 • Solving Using the Quadratic Formula • Approximating Solutions

  3. Solving Using the Quadratic Formula Each time we solve by completing the square, the procedure is the same. When a procedure is repeated many times, a formula can often be developed to speed up our work. If we begin with a quadratic equation in standard form, ax2 + bx + c = 0, and solve by completing the square we arrive at the quadratic formula.

  4. The Quadratic Formula The solutions of ax2 + bx + c = 0, are given by

  5. Solve 3x2 + 5x = 2 using the quadratic formula. Solution Put it in Standard Form and determine a, b, and c (1 point) Substituting

  6. Substitute a, b, and c into the quadratic formula (1 point).

  7. Simplify and state the solutions. ( 1 point)

  8. To Solve a Quadratic Equation • If b = 0, isolate x2 and use the principle of square roots to root both sides. • If b is not 0, try factoring and using the principle of zero products. • If b is not zero and the quadratic is not easily factorable, write the equation in the form x2 + bx + c = 0, if b is even, try completing the square. • 4. If b is not zero, the quadratic is not easily factorable, and b is not even, then use the quadratic formula. • Note: The quadratic formula can always be used and so if time constraints are high, you can always skip 1-3 and try it as a first resort.

  9. Recall that a second-degree polynomial in one variable is said to be quadratic. Similarly, a second-degree polynomial function in one variable is said to be a quadratic function.

  10. Solve x2 + 7 = 2x using the quadratic formula. Solution Put it in Standard Form and determine a, b, and c (1 point)

  11. Substitute a, b, and c into the quadratic formula (1 point).

  12. Simplify and state the solutions. ( 1 point)

  13. Solve x2 + 7 = 2x by any method. Solution Check if b is 0. If so, isolate x2 and root both sides. Since b is not 0, check for factoring, a diamond shows it is not factorable. Get standard form and check if b is even for completing the square. Since b is even we complete the square.

  14. Solve x2 + 7 = 2x by any method. 1. Get the form x2 + bx = c (1 point)

  15. Take ½ of b, square it, and add it to both sides. (complete the square) (1 point)

  16. Use the principle of powers to root both sides. Move the constant. State the answer.) (1 point)

More Related