1 / 10

Bellringer

Bellringer. Solve the equation and graph the related function. a. What is the maximum number of x-intercepts possible? b. How many x-intercepts are there and where are they? HINT: The factored form of the polynomial is: (x+2)³(x-3)².

moses-barnett
Download Presentation

Bellringer

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. Bellringer Solve the equation and graph the related function. a. What is the maximum number of x-intercepts possible? b. How many x-intercepts are there and where are they? HINT: The factored form of the polynomial is: (x+2)³(x-3)²

  2. 4-2A Graphing Calculators: Graphing Quadratic Functions • Solve 0 = -5x² + 3.27x + 19.11 • Do #2-10 evens on page 186

  3. 4-2 Quadratic Equations and Inequalities • Solve Quadratic Equations by: • Factoring • Graphing • Use the quadratic formula • Completing the square

  4. Quadratic Formula

  5. Solve • -10x² - 50x + 1500 = 0 • 4x² - 8x + 3 = 0 • x² - 6x + 13 = 0

  6. Discriminants Discriminant Nature of the Roots b² - 4ac > 0 two distinct real roots b² - 4ac = 0 exactly one real root b² - 4ac < 0 no real roots (imaginary)

  7. Complex Conjugates Theorem • If a + bi is a root of a polynomial equation, then a – bi is also a root of the equation.

  8. Graph: y > x² + 8x – 20Without a calculator! • Find the x-intercepts using by factoring or using the quadratic formula. • Find the y-intercept (substitute 0 in for x). • Find the vertex: Find the first derivative of the equation, solve for x, and then substitute that value into the original equation for x to get the y-coordinate of the vertex. • Graph! • Finally - Shade

  9. Example • Solve the equation by completing the square: 2x² + 11x – 21 = 0.

  10. The end!!

More Related