Your SlideShare is downloading. ×
4.1 quadratic functions and transformations
4.1 quadratic functions and transformations
4.1 quadratic functions and transformations
4.1 quadratic functions and transformations
4.1 quadratic functions and transformations
4.1 quadratic functions and transformations
4.1 quadratic functions and transformations
4.1 quadratic functions and transformations
4.1 quadratic functions and transformations
4.1 quadratic functions and transformations
4.1 quadratic functions and transformations
4.1 quadratic functions and transformations
4.1 quadratic functions and transformations
4.1 quadratic functions and transformations
Upcoming SlideShare
Loading in...5
×

Thanks for flagging this SlideShare!

Oops! An error has occurred.

×
Saving this for later? Get the SlideShare app to save on your phone or tablet. Read anywhere, anytime – even offline.
Text the download link to your phone
Standard text messaging rates apply

4.1 quadratic functions and transformations

22,874

Published on

Published in: Education, Technology
1 Comment
2 Likes
Statistics
Notes
  • SUPER helpful ! Thanks a lot !!!!
       Reply 
    Are you sure you want to  Yes  No
    Your message goes here
No Downloads
Views
Total Views
22,874
On Slideshare
0
From Embeds
0
Number of Embeds
1
Actions
Shares
0
Downloads
205
Comments
1
Likes
2
Embeds 0
No embeds

Report content
Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
No notes for slide

Transcript

  • 1. CHAPTER 4 QUADRATIC FUNCTIONSAND EQUATIONS4.1 Quadratic Functions and Transformations
  • 2. DEFINITIONS A parabola is the graph of a quadratic function.  A parabola is a “U” shaped graph  The parent Quadratic Function is Vertex at (0, 0) Axis of Symmetry at x = 0
  • 3. DEFINITIONS The vertex form of a quadratic function makes it easy to identify the transformations The axis of symmetry is a line that divides the parabola into two mirror images (x = h) The vertex of the parabola is (h, k) and it represents the intersection of the parabola and the axis of symmetry.
  • 4. REFLECTION, STRETCH, AND COMPRESSION Working with functions of the form  The determines the “width” of the parabola  If the the graph is vertically stretched (makes the “U” narrow)  If the graph is vertically compressed (makes the “U” wide)  If a is negative, the graph is reflected over the x– axis
  • 5. MINIMUM AND MAXIMUM VALUES The minimum value of a function is the least y – value of the function; it is the y – coordinate of the lowest point on the graph. The maximum value of a function is the greatest y – value of the function; it is the y– coordinate of the highest point on the graph. For quadratic functions the minimum or maximum point is always the vertex, thus the minimum or maximum value is always the y – coordinate of the vertex
  • 6. TRANSFORMATIONS – USING VERTEX FORM  Remember transformations from Chapter 2  The vertex form makes identifying transformations easy  a gives you information about stretch, compression, and reflection over the x – axis  h gives you information about the horizontal shift  k gives you information about the vertical shift  The vertex is at (h, k)  The axis of symmetry is at x = h
  • 7. TRANSFORMATIONS – USING VERTEX FORM Graphing Quadratic Functions: 1. Identify and Plot the vertex and axis of symmetry 2. Set up a Table of Values. Choose x – values to the right and left of the vertex and find the corresponding y – values 3. Plot the points and sketch the parabola
  • 8. EXAMPLE: GRAPH EACH FUNCTION. DESCRIBEHOW IT WAS TRANSLATED FROM
  • 9. EXAMPLE: GRAPH EACH FUNCTION. DESCRIBEHOW IT WAS TRANSLATED FROM
  • 10. EXAMPLE: GRAPH EACH FUNCTION. DESCRIBEHOW IT WAS TRANSLATED FROM
  • 11. EXAMPLE: GRAPH EACH FUNCTION. DESCRIBEHOW IT WAS TRANSLATED FROM
  • 12. TRANSFORMATIONS – USING VERTEX FORM Writing the equations of Quadratic Functions: 1. Identify the vertex (h, k) 2. Choose another point on the graph (x, y) 3. Plug h, k, x, and y into and solve for a 4. Use h, k, and a to write the vertex form of the quadratic function
  • 13. EXAMPLE: WRITE A QUADRATIC FUNCTION TOMODEL EACH GRAPH
  • 14. EXAMPLE: WRITE A QUADRATIC FUNCTION TOMODEL EACH GRAPH

×