1 / 10

Understanding the Discriminant: What to Expect for Quadratic Equations

This guide provides a comprehensive overview of using the discriminant to determine the number of solutions for quadratic equations. Explore how the value of the discriminant—expressed as b² - 4ac—indicates whether there are two solutions, one solution, or no real solution. This essential concept helps in graphing quadratic functions and identifying x-intercepts. We include examples and checkpoints to enhance understanding and application of the discriminant in different quadratic scenarios.

remedios-petty
Télécharger la présentation

Understanding the Discriminant: What to Expect for Quadratic Equations

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. WARM UP 4 WHAT TO EXPECT FOR THE REST OF THE YEAR

  2. WARM UP 3 WHAT TO EXPECT FOR THE REST OF THE YEAR

  3. WARM UP 2 WHAT TO EXPECT FOR THE REST OF THE YEAR

  4. WARM UP 1 WHAT TO EXPECT FOR THE REST OF THE YEAR

  5. WARM UP 0 WHAT TO EXPECT FOR THE REST OF THE YEAR

  6. 9.7 Using the Discriminant GOAL Use the discriminant to determine the number of solutions of a quadratic equation. KEY WORDS Discriminant

  7. 9.7 Using the Discriminant In the quadratic formula, the expression inside the radical is the DISCRIMINANT. x = DISCRIMINANT - 4ac

  8. 9.7 Using the Discriminant • Consider the quadratic equation ax2+ bx + c = 0 • If the value of b2 – 4ac is positive, then the equation has two solutions. • If the value of b2 – 4ac is zero, then the equation has one solution. • If the value of b2 – 4ac is negative, then the equation has no real solution. THE NUMBER OF SOLUTIONS OF A QUADRATIC EQUATION

  9. 9.7 Using the Discriminant x-intercept Because each solution of ax2 + bx + c = 0 represents an x-intercept of y = ax2 + bx + c, you can use the discriminant to determine the number of times the graph of a quadratic function intersects the x-axis. These points are called the x-intercepts or roots. x-intercept (-1, 0) (2, 0) y = x2 – x - 2

  10. 9.7 Using the Discriminant Checkpoint Find the Number of Solutions. Find the value of the discriminant. Then use the value to determine whether the equation has two solutions, one solution, or no real solution. -3x2+2x -5= 0 2x2-3x -4= 0 5x2-4x +2= 0

More Related