Question

using quantitative reasoning
hope researches the impact of one variable on another. she graphs the data from her research and sees that the data forms a shape that is similar to an arch. what conclusion can hope draw from her graph?

Explanation:

An arch - shaped graph (a parabola opening downwards) in the context of a relationship between two variables implies a quadratic relationship. In a quadratic relationship of the form \(y = ax^{2}+bx + c\) with \(a<0\), as the independent variable \(x\) increases initially, the dependent variable \(y\) increases up to a maximum point (vertex of the parabola), and then as \(x\) continues to increase, \(y\) decreases.

Answer:

Hope can conclude that there is a quadratic relationship between the two variables. Initially, as one variable (independent variable) increases, the other variable (dependent variable) increases, but after a certain point (the vertex of the arch - shaped graph), as the independent variable continues to increase, the dependent variable decreases.