1 / 12

Unit #3: Quadratics 5-8: The Quadratic Formula

Unit #3: Quadratics 5-8: The Quadratic Formula. Essential Question: What are some things the discriminate is used for?. 5-8: The Quadratic Formula. Sometimes you’ll run into a quadratic expression that cannot be factored. For example: x 2 + 10x + 4 = 0

kasa
Download Presentation

Unit #3: Quadratics 5-8: The Quadratic Formula

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. Unit #3: Quadratics5-8: The Quadratic Formula Essential Question: What are some things the discriminate is used for?

  2. 5-8: The Quadratic Formula • Sometimes you’ll run into a quadratic expression that cannot be factored. • For example: x2 + 10x + 4 = 0 • There is no combination of numbers that multiplies to get 4 and adds to 10. • Yet, there are real numbers that exist for x to make that a true statement. • There exists a formula that allows you to find the solutions for any quadratic equation, called the QUADRATIC FORMULA

  3. 5-8: The Quadratic Formula • A quadratic equation written in standard form ax2 + bx + c = 0can be solved with the quadratic equation

  4. 5-8: The Quadratic Formula • The “b2 – 4ac” underneath the square root is called the discriminant. • The discriminant tells us how many (and what type) of solutions we get from the quadratic equation Discriminant

  5. 5-8: The Quadratic Equation • The Discriminant • Determine the type and number of solutions of x2 + 6x + 8 = 0 • a = 1, b = 6, c = 8 • Two real solutions

  6. 5-8: The Quadratic Equation • Determine the type and number of solutions • x2 + 6x + 9 = 0 • x2 + 6x + 10 = 0 62 – 4(1)(9) = 36 – 36 = 0 1 Real Solution 62 – 4(1)(10) = 36 – 40 = -4 2 Imaginary Solutions

  7. 5-8: The Quadratic Formula • What is the quadratic equation?:

  8. 5-8: The Quadratic Formula • Empirical verification that the formula works • x2 + 8x + 12 = 0 can be factored as • (x + 6)(x + 2) = 0 meaning • x = -6 OR x = -2 • a = 1, b = 8, c = 12

  9. 5-8: The Quadratic Formula • Using the quadratic formula to solve a problem that can’t be factored • x2 + 10x + 4 = 0 • a = 1, b = 10, c = 4

  10. 5-8: The Quadratic Formula • Another equation that can’t be factored • 2x2 - 6x + 1 = 0 • a = 2, b = -6, c = 1

  11. 5-8: The Quadratic Formula • Use the quadratic equation to solve 2x2 = –6x – 7

  12. 5-8: The Quadratic Formula • Assignment • Page 293 • Problems 1 – 21, 31 – 39 (odds) • Show your work • Ignore directions in 23-29 to approximate radical solutions • Leave your answers in simplest radical form

More Related