Graphing Quadratic Functions & Exploring Shifts
*The basic graph that one would use to compare others to is x^2. Rules:
1. Any number not in parentheses indicates that the graph moves up or down. Positive numbers go up, negatives go down. ex. y= x^2 + 4 The graph would move up 4 on the y-axis because there are no parentheses.
2. A number inside the parentheses after x^2 indicates that the graph moves left or right. Negative numbers move right, positives move left ( opposites). ex. y= (x^2 - 3) The graph moved right on the graph because it is in parentheses, and the "-3" changes to plus/positive 3 to become opposite.
3. If you make the equation negative, the graph will flip, making the shape open downwards. ex. y= - x^2 This would cause the graph to simply flip upside down from the original x^2 position.
4. You can combine your knowledge of all the rules above to solve this last example. ex. y= - (x^2 + 2) For this problem, the graph flips because its negative and goes to negative 2 on the x-axis because the positive 2 in the parentheses indicates that the graph moves left.
Here is the link to our tutorial:
Enjoy!
- Anna & DiBella
*The basic graph that one would use to compare others to is x^2.
Rules:
1. Any number not in parentheses indicates that the graph moves up or down. Positive numbers go up, negatives go down.
ex. y= x^2 + 4
The graph would move up 4 on the y-axis because there are no parentheses.
2. A number inside the parentheses after x^2 indicates that the graph moves left or right. Negative numbers move right, positives move left ( opposites).
ex. y= (x^2 - 3)
The graph moved right on the graph because it is in parentheses, and the "-3" changes to plus/positive 3 to become opposite.
3. If you make the equation negative, the graph will flip, making the shape open downwards.
ex. y= - x^2
This would cause the graph to simply flip upside down from the original x^2 position.
4. You can combine your knowledge of all the rules above to solve this last example.
ex. y= - (x^2 + 2)
For this problem, the graph flips because its negative and goes to negative 2 on the x-axis because the positive 2 in the parentheses indicates that the graph moves left.
Here is the link to our tutorial:
Enjoy!
- Anna & DiBella
http://www.pascack.k12.nj.us/7042081822151940/lib/7042081822151940/anna_and_dibella.mov