Quadratic Functions and Models: Characteristics and Equations

Explore writing quadratic functions given specific characteristics such as vertices, x-intercepts, and points passed through. Learn how to form equations in vertex form, intercept form, and standard form by plugging in values and solving systems of equations. Practice creating quadratic functions with varying properties to understand their graphical representations.

• Quadratic Functions
• Equations
• Graphs
• Characteristics
• Vertex Form

lish_do Follow

Uploaded on Sep 13, 2024 | 0 Views

Download Presentation

Please find below an Image/Link to download the presentation.

The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author. Download presentation by click this link. If you encounter any issues during the download, it is possible that the publisher has removed the file from their server.

Presentation Transcript

1. 4.10: Write Quadratic Functions and Models HW: p.312 313 (4, 12, 18, 22, 28, 34) Test 4.7-4.10: Wednesday

2. Write a quadratic function whose graph has the given characteristics. 1.) Vertex: (1, -2) and passes through: (3, 2). Vertex form: y = a(x h)2 + k ; plug in values to find a, then write the equation.

3. Write a quadratic function whose graph has the given characteristics. 2.) Vertex: (4, -5) and passes through: (2, -1).

4. Write a quadratic function whose graph has the given characteristics. 3.) x-intercepts: -1 and 4 and passes through: (3, 2). Intercept form: y = a(x p)(x q) ; plug in values to find a, then write the equation.

5. Write a quadratic function whose graph has the given characteristics. 4.) x-intercepts: -2 and 5 and passes through (6, 2).

6. Write a quadratic function whose graph has the given characteristics. 5.) Passes through: (-1, -3), (0, -4), (2, 6). Using Standard Form: y = ax2 + bx + c ; plug in the coordinates of each point to obtain a system of three equations. Solve the system and write the equation.

7. Write a quadratic function whose graph has the given characteristics. 6.) Passes through: (-1, 0), (1, -2), (2, -15).

8. Write a quadratic function whose graph has the given characteristics. 7.) Vertex: (1, 6)and passes through: (-1, 2) 8.) x-intercepts: -3, 3 and passes through: (1, -4) 9.) Passes through: (-2, -13), (2, 3), (4, 5).