Quadratic Relations 1st 2nd differences

In summary, the conversation discusses calculating first and second differences and identifying linear and nonlinear relationships in data sets. It also mentions determining slopes in nonlinear relationships. The first difference is the difference between successive numbers, and a linear relationship has numbers that increase by the same value while a nonlinear relationship does not. The slope is the difference on Y divided by the difference on X.
  • #1
rachelg2004
1
0
can someone help me

a) for each set of data, calculate the first differences and identify the linear and nonlinear relations
b) for the nonlinear relations determine the second differences and identify the quadratic relations

1)
x 5 6 8 11
y -2 -3 -5 -8

then it says to determine the slope

I DONT GET THIS AT ALL AND I"M SO FRUSTERATED! HELP! :cry:
 
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  • #2
The first difference, probably, is simply the difference between successive numbers.

For the rest, the vocabulary used seems to be specific to your course. (note that I am french)
You should read the definitions and apply them.

If you want to post again the question, I suggest that you write also the definitions from your handbook.
Then, someone could explain you what it means.

I guess your question might be related to curve fitting, but I cannot be sure.
Indicate also the background to increase your chances to find some help.
 
  • #3
rachelg2004 said:
can someone help me

a) for each set of data, calculate the first differences and identify the linear and nonlinear relations
b) for the nonlinear relations determine the second differences and identify the quadratic relations

1)
x 5 6 8 11
y -2 -3 -5 -8

then it says to determine the slope

I DONT GET THIS AT ALL AND I"M SO FRUSTERATED! HELP! :cry:

Linear relationship: The numbers always increase by the same value. Like:
2, 4, 6, 8, 10, 12 ...
or
5, 8, 11, 14, 17, 20 ...

Nonlinear: Hmmm, I wonder... maybe when it isn't constant?:
1,2,4,8,16
or
1,3,6,10,15

The slope is the difference on Y divided by the difference on X. For your answer, it's probably just something like:
(6 - 5) / 1 = 1
 

1. What are quadratic relations?

Quadratic relations are mathematical relationships between two variables that can be represented by a quadratic function. These functions have the form f(x) = ax^2 + bx + c, where a, b, and c are constants.

2. What are first and second differences in quadratic relations?

First and second differences refer to the changes in the y-values of a quadratic function as the x-values increase by one unit. The first difference is the difference between consecutive y-values, while the second difference is the difference between consecutive first differences.

3. How do you find the first and second differences in a quadratic relation?

To find the first differences, simply subtract each y-value from the next consecutive y-value. To find the second differences, subtract each first difference from the next consecutive first difference. This can be represented in a table or in a graph.

4. What do the first and second differences tell us about a quadratic relation?

The first differences can tell us whether the quadratic relation is increasing or decreasing. If the first differences are constant, the relation is linear. If the first differences are increasing or decreasing, the relation is quadratic. The second differences can tell us whether the quadratic relation is concave up or concave down. If the second differences are constant, the relation is linear. If the second differences are positive, the relation is concave up. If the second differences are negative, the relation is concave down.

5. How can first and second differences be used to graph a quadratic relation?

First and second differences can be used to find the x-intercepts, y-intercepts, and vertex of a quadratic relation. The x-intercepts can be found by setting the function equal to zero and solving for x. The y-intercept can be found by plugging in x=0 into the function. The x-coordinate of the vertex can be found by taking the average of the x-values of the two x-intercepts. The y-coordinate of the vertex can be found by plugging in the x-coordinate of the vertex into the function.

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