Solution Found!
Consider the following quadratic models:(1) y = 1 - 2x +
Chapter 12, Problem 52E(choose chapter or problem)
Consider the following quadratic models:
(1) y = 1 - 2x + \(x^2\)
(2) y = 1 + 2x + \(x^2\)
(3) y = 1 + \(x^2\)
(4) y = 1 - \(x^2\)
(5) y = 1 + \(3x^2\)
a. Graph each of the quadratic models, side by side, on the same sheet of graph paper.
b. What effect does the first-order term (2x) have on the graph of the curve?
c. What effect does the second-order term (\(x^2\)) have on the graph of the curve?
Questions & Answers
QUESTION:
Consider the following quadratic models:
(1) y = 1 - 2x + \(x^2\)
(2) y = 1 + 2x + \(x^2\)
(3) y = 1 + \(x^2\)
(4) y = 1 - \(x^2\)
(5) y = 1 + \(3x^2\)
a. Graph each of the quadratic models, side by side, on the same sheet of graph paper.
b. What effect does the first-order term (2x) have on the graph of the curve?
c. What effect does the second-order term (\(x^2\)) have on the graph of the curve?
ANSWER:Step 1 of 6
We consider models that allows for curvature in the 2-dimensional relationship between
y and an independent variable. Each of these models is a second-order model because it
will include a 
First, we consider a model that includes only one independent variable x. The form of
this model, called the quadratic model, is
The term involving
hypothesize curvature of the response model relating y to x. When the curve opens
upward, the sign of 
negative.