1 / 23

Graphs of Quadratic Equations

Module 3 Lesson 5:. Graphs of Quadratic Equations. a. h. k. Table of Contents Slides 3-9: Review Standard Form Slides 10-14: Review Vertex Form Slides 15-21: Review Transformations Slide 22: Find the Equation From a Graph

stephanie-carpenter
Télécharger la présentation

Graphs of 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. Module 3 Lesson 5: Graphs of Quadratic Equations a h k

  2. Table of Contents • Slides 3-9: Review Standard Form • Slides 10-14: Review Vertex Form • Slides 15-21: Review Transformations • Slide 22: Find the Equation From a Graph • Slide 23: Find the Vertex and y-Intercept from an Equation • Audio/Video and Interactive Sites • Slide 4: Gizmos • Slide 6: Gizmos • Slide 12: Gizmos

  3. Explore Quadratic Equations In Standard Form

  4. For a more straightforward explanation on the affect of A, B, and C. Look at the following Gizmo. Gizmo: How A, B, and C affect the quadratic function. To explore the affect the variables A, B, and C have on the graph, play the Zap It game found at the following link. Zap It Game

  5. On your graphing calculator… Graph y= x2 Graph y = -x2 What do you see? What is A in the above two equations and how does it affect the graph?

  6. In this equation, A = -1 In this equation, A = 1 Gizmo: Standard Form, Vertex, and Intercepts Gizmo: Standard Form, Vertex, and Intercepts (B)

  7. f(x) = Ax2+ Bx + C If A = 0, the graph is not quadratic, it is linear. If A is not 0, B and/or C can be 0 and the function is still a quadratic function. If A < 0, The parabola opens down, like an umbrella. If A > 0, The parabola opens up, like an bowl. In this equation, A = -1 In this equation, A = 1

  8. When "a" is positive, the graph of y = ax2 + bx + c opens upward and the vertex is the lowest point on the curve. As the value of the coefficient "a" gets larger, |a| > 1, the parabola narrows. As the value of the coefficient “a” gets smaller, | a | is between 0 and 1, the parabola widens.

  9. For the graph of y = Ax2 + Bx + C If C is positive, the graph shifts up C units If C is negative, the graph shifts down C units Since C is negative, -5, the graph shifts down 5 units Since C is positive, 12, the graph shifts up 12 units. Note: This graph would open upside down since A is -2 Since C is negative, -8, the graph shifts down 8 units

  10. Vertex Form of the Quadratic Equation

  11. The Vertex Form of quadratic functions is often used, especially when we want to see how a graph behaves as values change. y=Ax2 + Bx + C (Standard Form) Can be factored y = a(x - h)2 + k (Vertex Form) Notice: If you are given the equation in Vertex Form, you can FOIL the (x-h) part, distribute a, and then combine like terms to get back to Standard Form.

  12. Gizmo: Vertex Form, Vertex, Intercepts Gizmo: Vertex Form, Vertex, Intercepts (B)

  13. Practice Assignment 1—State whether each Quadratic Function is in Vertex Form, Quadratic Form, or Neither. • Quadratic Form • b. Vertex Form • c. Neither

  14. Practice Assignment 1 Answers—State whether each Quadratic Function is in Vertex Form, Quadratic Form, or Neither. • Quadratic Form • b. Vertex Form • c. Neither

  15. Transformation affects of a, h, and k.

  16. When a is positive Graph opens up. As a increases, graph gets narrower As a decreases, graph gets wider When a and h are positive: a(x – (+h))2 = a(x – h)2 Graph moves right h units. When a is negative and h is positive: -a(x – (+h))2 = -a(x – h)2 Graph moves right h units. When k is positive Graph moves up regardless of what a and h are. When k is negative Graph moves down regardless of what a and h are. When a is positive and h is negative: a(x – (-h))2 = a(x + h)2 Graph moves left h units. When a is negative Graph opens down. As a increases (approaches 0), graph gets wider As a decreases (approaches negative infinity), graph gets narrower When a and h are negative: -a(x – (-h))2 = a(x + h)2 Graph moves left h units.

  17. When a is positive Graph opens up. As a increases, graph gets narrower As a decreases, graph gets wider

  18. When a is negative Graph opens down. As a increases (approaches 0), graph gets wider As a decreases (approaches negative infinity), graph gets narrower

  19. +k When k is positive Graph moves up regardless of what a and h are. - k When k is negative Graph moves down regardless of what a and h are.

  20. When a and h are positive: a(x – (+h))2 = a(x – h)2 Graph moves right h units. When a is negative and h is positive: -a(x – (+h))2 = -a(x – h)2 Graph moves right h units.

  21. When a is positive and h is negative: a(x – (-h))2 = a(x + h)2 Graph moves left h units. When a and h are negative: -a(x – (-h))2 = a(x + h)2 Graph moves left h units.

  22. Find the equation of the following graph. Start by writing down the generic vertex form equation. Note: a will be a negative since the graph is upside down. Identify the vertex: (1, 2) Identify the y-intercept: (0, -1) Fill in all the information you just found and solve for a. From the vertex: h = 1 and k = 2 From the y-intercept: x = 0 and y = -1 Simplify and Solve for a Therefore, the equation in vertex form is:

  23. Identify the vertex and y-intercept of the following equation. Identify the vertex: Identify the y-intercept: (0, -10.5) (h, k) (-3, -6)

More Related